Algebra Examples

$\begin{array}{c} x & y \\ 6 & 6 \\ 3 & 8 \\ 9 & 12 \end{array}$

Step 1

Check if the function rule is linear.

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Step 1.1

To find if the table follows a function rule, check to see if the values follow the linear form $y = a x + b$ .

$y = a x + b$

Step 1.2

Build a set of equations from the table such that $y = a x + b$ .

$6 = a (6) + b 8 = a (3) + b 12 = a (9) + b$

Step 1.3

Calculate the values of $a$ and $b$ .

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Step 1.3.1

Solve for $b$ in $6 = a (6) + b$ .

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Step 1.3.1.1

Rewrite the equation as $a (6) + b = 6$ .

$a (6) + b = 6$

$8 = a (3) + b$

$12 = a (9) + b$

Step 1.3.1.2

Move $6$ to the left of $a$ .

$6 a + b = 6$

$8 = a (3) + b$

$12 = a (9) + b$

Step 1.3.1.3

Subtract $6 a$ from both sides of the equation.

$b = 6 - 6 a$

$8 = a (3) + b$

$12 = a (9) + b$

$b = 6 - 6 a$

$8 = a (3) + b$

$12 = a (9) + b$

Step 1.3.2

Replace all occurrences of $b$ with $6 - 6 a$ in each equation.

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Step 1.3.2.1

Replace all occurrences of $b$ in $8 = a (3) + b$ with $6 - 6 a$ .

$8 = a (3) + 6 - 6 a$

$b = 6 - 6 a$

$12 = a (9) + b$

Step 1.3.2.2

Simplify $8 = a (3) + 6 - 6 a$ .

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Step 1.3.2.2.1

Simplify the left side.

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Step 1.3.2.2.1.1

Remove parentheses.

$8 = a (3) + 6 - 6 a$

$b = 6 - 6 a$

$12 = a (9) + b$

$8 = a (3) + 6 - 6 a$

$b = 6 - 6 a$

$12 = a (9) + b$

Step 1.3.2.2.2

Simplify the right side.

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Step 1.3.2.2.2.1

Simplify $a (3) + 6 - 6 a$ .

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Step 1.3.2.2.2.1.1

Move $3$ to the left of $a$ .

$8 = 3 a + 6 - 6 a$

$b = 6 - 6 a$

$12 = a (9) + b$

Step 1.3.2.2.2.1.2

Subtract $6 a$ from $3 a$ .

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = a (9) + b$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = a (9) + b$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = a (9) + b$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = a (9) + b$

Step 1.3.2.3

Replace all occurrences of $b$ in $12 = a (9) + b$ with $6 - 6 a$ .

$12 = a (9) + 6 - 6 a$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.2.4

Simplify $12 = a (9) + 6 - 6 a$ .

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Step 1.3.2.4.1

Simplify the left side.

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Step 1.3.2.4.1.1

Remove parentheses.

$12 = a (9) + 6 - 6 a$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = a (9) + 6 - 6 a$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.2.4.2

Simplify the right side.

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Step 1.3.2.4.2.1

Simplify $a (9) + 6 - 6 a$ .

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Step 1.3.2.4.2.1.1

Move $9$ to the left of $a$ .

$12 = 9 a + 6 - 6 a$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.2.4.2.1.2

Subtract $6 a$ from $9 a$ .

$12 = 3 a + 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = 3 a + 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = 3 a + 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = 3 a + 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$12 = 3 a + 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3

Solve for $a$ in $12 = 3 a + 6$ .

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Step 1.3.3.1

Rewrite the equation as $3 a + 6 = 12$ .

$3 a + 6 = 12$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3.2

Move all terms not containing $a$ to the right side of the equation.

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Step 1.3.3.2.1

Subtract $6$ from both sides of the equation.

$3 a = 12 - 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3.2.2

Subtract $6$ from $12$ .

$3 a = 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$3 a = 6$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3.3

Divide each term in $3 a = 6$ by $3$ and simplify.

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Step 1.3.3.3.1

Divide each term in $3 a = 6$ by $3$ .

$\frac{3 a}{3} = \frac{6}{3}$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3.3.2

Simplify the left side.

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Step 1.3.3.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.3.3.2.1.1

Cancel the common factor.

$\frac{3 a}{3} = \frac{6}{3}$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{6}{3}$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$a = \frac{6}{3}$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$a = \frac{6}{3}$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.3.3.3

Simplify the right side.

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Step 1.3.3.3.3.1

Divide $6$ by $3$ .

$a = 2$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$a = 2$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$a = 2$

$8 = - 3 a + 6$

$b = 6 - 6 a$

$a = 2$

$8 = - 3 a + 6$

$b = 6 - 6 a$

Step 1.3.4

Replace all occurrences of $a$ with $2$ in each equation.

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Step 1.3.4.1

Replace all occurrences of $a$ in $8 = - 3 a + 6$ with $2$ .

$8 = - 3 \cdot 2 + 6$

$a = 2$

$b = 6 - 6 a$

Step 1.3.4.2

Simplify the right side.

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Step 1.3.4.2.1

Simplify $- 3 \cdot 2 + 6$ .

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Step 1.3.4.2.1.1

Multiply $- 3$ by $2$ .

$8 = - 6 + 6$

$a = 2$

$b = 6 - 6 a$

Step 1.3.4.2.1.2

Add $- 6$ and $6$ .

$8 = 0$

$a = 2$

$b = 6 - 6 a$

$8 = 0$

$a = 2$

$b = 6 - 6 a$

$8 = 0$

$a = 2$

$b = 6 - 6 a$

Step 1.3.4.3

Replace all occurrences of $a$ in $b = 6 - 6 a$ with $2$ .

$b = 6 - 6 \cdot 2$

$8 = 0$

$a = 2$

Step 1.3.4.4

Simplify the right side.

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Step 1.3.4.4.1

Simplify $6 - 6 \cdot 2$ .

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Step 1.3.4.4.1.1

Multiply $- 6$ by $2$ .

$b = 6 - 12$

$8 = 0$

$a = 2$

Step 1.3.4.4.1.2

Subtract $12$ from $6$ .

$b = - 6$

$8 = 0$

$a = 2$

$b = - 6$

$8 = 0$

$a = 2$

$b = - 6$

$8 = 0$

$a = 2$

$b = - 6$

$8 = 0$

$a = 2$

Step 1.3.5

Since $8 = 0$ is not true, there is no solution.

No solution

Step 1.4

Since $y \neq y$ for the corresponding $x$ values, the function is not linear.

The function is not linear

Step 2

Check if the function rule is quadratic.

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Step 2.1

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{2} + b x + c$ .

$y = a x^{2} + b x + c$

Step 2.2

Build a set of $3$ equations from the table such that $y = a x^{2} + b x + c$ .

Step 2.3

Calculate the values of $a$ , $b$ , and $c$ .

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Step 2.3.1

Solve for $c$ in $6 = a \cdot 6^{2} + b (6) + c$ .

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Step 2.3.1.1

Rewrite the equation as $a \cdot 6^{2} + b (6) + c = 6$ .

$a \cdot 6^{2} + b (6) + c = 6$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.1.2

Simplify each term.

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Step 2.3.1.2.1

Raise $6$ to the power of $2$ .

$a \cdot 36 + b (6) + c = 6$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.1.2.2

Move $36$ to the left of $a$ .

$36 \cdot a + b (6) + c = 6$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.1.2.3

Move $6$ to the left of $b$ .

$36 a + 6 b + c = 6$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

$36 a + 6 b + c = 6$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.1.3

Move all terms not containing $c$ to the right side of the equation.

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Step 2.3.1.3.1

Subtract $36 a$ from both sides of the equation.

$6 b + c = 6 - 36 a$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.1.3.2

Subtract $6 b$ from both sides of the equation.

$c = 6 - 36 a - 6 b$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

$c = 6 - 36 a - 6 b$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

$c = 6 - 36 a - 6 b$

$8 = a \cdot 3^{2} + b (3) + c$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2

Replace all occurrences of $c$ with $6 - 36 a - 6 b$ in each equation.

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Step 2.3.2.1

Replace all occurrences of $c$ in $8 = a \cdot 3^{2} + b (3) + c$ with $6 - 36 a - 6 b$ .

$8 = a \cdot 3^{2} + b (3) + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.2

Simplify $8 = a \cdot 3^{2} + b (3) + 6 - 36 a - 6 b$ .

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Step 2.3.2.2.1

Simplify the left side.

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Step 2.3.2.2.1.1

Remove parentheses.

$8 = a \cdot 3^{2} + b (3) + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

$8 = a \cdot 3^{2} + b (3) + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.2.2

Simplify the right side.

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Step 2.3.2.2.2.1

Simplify $a \cdot 3^{2} + b (3) + 6 - 36 a - 6 b$ .

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Step 2.3.2.2.2.1.1

Simplify each term.

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Step 2.3.2.2.2.1.1.1

Raise $3$ to the power of $2$ .

$8 = a \cdot 9 + b (3) + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.2.2.1.1.2

Move $9$ to the left of $a$ .

$8 = 9 \cdot a + b (3) + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.2.2.1.1.3

Move $3$ to the left of $b$ .

$8 = 9 a + 3 b + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

$8 = 9 a + 3 b + 6 - 36 a - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.2.2.1.2

Simplify by adding terms.

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Step 2.3.2.2.2.1.2.1

Subtract $36 a$ from $9 a$ .

$8 = - 27 a + 3 b + 6 - 6 b$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.2.2.1.2.2

Subtract $6 b$ from $3 b$ .

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + c$

Step 2.3.2.3

Replace all occurrences of $c$ in $12 = a \cdot 9^{2} + b (9) + c$ with $6 - 36 a - 6 b$ .

$12 = a \cdot 9^{2} + b (9) + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.2.4

Simplify $12 = a \cdot 9^{2} + b (9) + 6 - 36 a - 6 b$ .

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Step 2.3.2.4.1

Simplify the left side.

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Step 2.3.2.4.1.1

Remove parentheses.

$12 = a \cdot 9^{2} + b (9) + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = a \cdot 9^{2} + b (9) + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.2.4.2

Simplify the right side.

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Step 2.3.2.4.2.1

Simplify $a \cdot 9^{2} + b (9) + 6 - 36 a - 6 b$ .

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Step 2.3.2.4.2.1.1

Simplify each term.

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Step 2.3.2.4.2.1.1.1

Raise $9$ to the power of $2$ .

$12 = a \cdot 81 + b (9) + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.2.4.2.1.1.2

Move $81$ to the left of $a$ .

$12 = 81 \cdot a + b (9) + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.2.4.2.1.1.3

Move $9$ to the left of $b$ .

$12 = 81 a + 9 b + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = 81 a + 9 b + 6 - 36 a - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.2.4.2.1.2

Simplify by adding terms.

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Step 2.3.2.4.2.1.2.1

Subtract $36 a$ from $81 a$ .

$12 = 45 a + 9 b + 6 - 6 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.2.4.2.1.2.2

Subtract $6 b$ from $9 b$ .

$12 = 45 a + 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = 45 a + 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = 45 a + 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = 45 a + 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = 45 a + 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$12 = 45 a + 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3

Solve for $a$ in $12 = 45 a + 3 b + 6$ .

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Step 2.3.3.1

Rewrite the equation as $45 a + 3 b + 6 = 12$ .

$45 a + 3 b + 6 = 12$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.2

Move all terms not containing $a$ to the right side of the equation.

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Step 2.3.3.2.1

Subtract $3 b$ from both sides of the equation.

$45 a + 6 = 12 - 3 b$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.2.2

Subtract $6$ from both sides of the equation.

$45 a = 12 - 3 b - 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.2.3

Subtract $6$ from $12$ .

$45 a = - 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$45 a = - 3 b + 6$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3

Divide each term in $45 a = - 3 b + 6$ by $45$ and simplify.

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Step 2.3.3.3.1

Divide each term in $45 a = - 3 b + 6$ by $45$ .

$\frac{45 a}{45} = \frac{- 3 b}{45} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.2

Simplify the left side.

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Step 2.3.3.3.2.1

Cancel the common factor of $45$ .

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Step 2.3.3.3.2.1.1

Cancel the common factor.

$\frac{45 a}{45} = \frac{- 3 b}{45} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 3 b}{45} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = \frac{- 3 b}{45} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = \frac{- 3 b}{45} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3

Simplify the right side.

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Step 2.3.3.3.3.1

Simplify each term.

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Step 2.3.3.3.3.1.1

Cancel the common factor of $- 3$ and $45$ .

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Step 2.3.3.3.3.1.1.1

Factor $3$ out of $- 3 b$ .

$a = \frac{3 (- b)}{45} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.1.2

Cancel the common factors.

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Step 2.3.3.3.3.1.1.2.1

Factor $3$ out of $45$ .

$a = \frac{3 (- b)}{3 (15)} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.1.2.2

Cancel the common factor.

$a = \frac{3 (- b)}{3 \cdot 15} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.1.2.3

Rewrite the expression.

$a = \frac{- b}{15} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = \frac{- b}{15} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = \frac{- b}{15} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.2

Move the negative in front of the fraction.

$a = - \frac{b}{15} + \frac{6}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.3

Cancel the common factor of $6$ and $45$ .

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Step 2.3.3.3.3.1.3.1

Factor $3$ out of $6$ .

$a = - \frac{b}{15} + \frac{3 (2)}{45}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.3.2

Cancel the common factors.

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Step 2.3.3.3.3.1.3.2.1

Factor $3$ out of $45$ .

$a = - \frac{b}{15} + \frac{3 \cdot 2}{3 \cdot 15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.3.2.2

Cancel the common factor.

$a = - \frac{b}{15} + \frac{3 \cdot 2}{3 \cdot 15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.3.3.3.1.3.2.3

Rewrite the expression.

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

$a = - \frac{b}{15} + \frac{2}{15}$

$8 = - 27 a - 3 b + 6$

$c = 6 - 36 a - 6 b$

Step 2.3.4

Replace all occurrences of $a$ with $- \frac{b}{15} + \frac{2}{15}$ in each equation.

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Step 2.3.4.1

Replace all occurrences of $a$ in $8 = - 27 a - 3 b + 6$ with $- \frac{b}{15} + \frac{2}{15}$ .

$8 = - 27 (- \frac{b}{15} + \frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2

Simplify the right side.

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Step 2.3.4.2.1

Simplify $- 27 (- \frac{b}{15} + \frac{2}{15}) - 3 b + 6$ .

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Step 2.3.4.2.1.1

Simplify each term.

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Step 2.3.4.2.1.1.1

Apply the distributive property.

$8 = - 27 (- \frac{b}{15}) - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.3.4.2.1.1.2.1

Move the leading negative in $- \frac{b}{15}$ into the numerator.

$8 = - 27 \frac{- b}{15} - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.2.2

Factor $3$ out of $- 27$ .

$8 = 3 (- 9) (\frac{- b}{15}) - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.2.3

Factor $3$ out of $15$ .

$8 = 3 \cdot (- 9 \frac{- b}{3 \cdot 5}) - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.2.4

Cancel the common factor.

$8 = 3 \cdot (- 9 \frac{- b}{3 \cdot 5}) - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.2.5

Rewrite the expression.

$8 = - 9 \frac{- b}{5} - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = - 9 \frac{- b}{5} - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.3

Combine $- 9$ and $\frac{- b}{5}$ .

$8 = \frac{- 9 (- b)}{5} - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.4

Multiply $- 1$ by $- 9$ .

$8 = \frac{9 b}{5} - 27 (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.5

Cancel the common factor of $3$ .

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Step 2.3.4.2.1.1.5.1

Factor $3$ out of $- 27$ .

$8 = \frac{9 b}{5} + 3 (- 9) (\frac{2}{15}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.5.2

Factor $3$ out of $15$ .

$8 = \frac{9 b}{5} + 3 \cdot (- 9 \frac{2}{3 \cdot 5}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.5.3

Cancel the common factor.

$8 = \frac{9 b}{5} + 3 \cdot (- 9 \frac{2}{3 \cdot 5}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.5.4

Rewrite the expression.

$8 = \frac{9 b}{5} - 9 (\frac{2}{5}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = \frac{9 b}{5} - 9 (\frac{2}{5}) - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.6

Combine $- 9$ and $\frac{2}{5}$ .

$8 = \frac{9 b}{5} + \frac{- 9 \cdot 2}{5} - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.7

Multiply $- 9$ by $2$ .

$8 = \frac{9 b}{5} + \frac{- 18}{5} - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.1.8

Move the negative in front of the fraction.

$8 = \frac{9 b}{5} - \frac{18}{5} - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = \frac{9 b}{5} - \frac{18}{5} - 3 b + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.2

To write $- 3 b$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 = \frac{9 b}{5} - 3 b \cdot \frac{5}{5} - \frac{18}{5} + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.3

Combine $- 3 b$ and $\frac{5}{5}$ .

$8 = \frac{9 b}{5} + \frac{- 3 b \cdot 5}{5} - \frac{18}{5} + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.4

Combine the numerators over the common denominator.

$8 = \frac{9 b - 3 b \cdot 5}{5} - \frac{18}{5} + 6$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.5

Combine the numerators over the common denominator.

$8 = 6 + \frac{9 b - 3 b \cdot 5 - 18}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.6

Multiply $5$ by $- 3$ .

$8 = 6 + \frac{9 b - 15 b - 18}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.7

Subtract $15 b$ from $9 b$ .

$8 = 6 + \frac{- 6 b - 18}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.8

Factor $6$ out of $- 6 b - 18$ .

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Step 2.3.4.2.1.8.1

Factor $6$ out of $- 6 b$ .

$8 = 6 + \frac{6 (- b) - 18}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.8.2

Factor $6$ out of $- 18$ .

$8 = 6 + \frac{6 (- b) + 6 (- 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.8.3

Factor $6$ out of $6 (- b) + 6 (- 3)$ .

$8 = 6 + \frac{6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = 6 + \frac{6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.9

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 = 6 \cdot \frac{5}{5} + \frac{6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.10

Simplify terms.

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Step 2.3.4.2.1.10.1

Combine $6$ and $\frac{5}{5}$ .

$8 = \frac{6 \cdot 5}{5} + \frac{6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.10.2

Combine the numerators over the common denominator.

$8 = \frac{6 \cdot 5 + 6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = \frac{6 \cdot 5 + 6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.11

Simplify the numerator.

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Step 2.3.4.2.1.11.1

Factor $6$ out of $6 \cdot 5 + 6 (- b - 3)$ .

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Step 2.3.4.2.1.11.1.1

Factor $6$ out of $6 \cdot 5$ .

$8 = \frac{6 (5) + 6 (- b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.11.1.2

Factor $6$ out of $6 (5) + 6 (- b - 3)$ .

$8 = \frac{6 (5 - b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = \frac{6 (5 - b - 3)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.11.2

Subtract $3$ from $5$ .

$8 = \frac{6 (- b + 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = \frac{6 (- b + 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.12

Simplify with factoring out.

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Step 2.3.4.2.1.12.1

Factor $- 1$ out of $- b$ .

$8 = \frac{6 (- (b) + 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.12.2

Rewrite $2$ as $- 1 (- 2)$ .

$8 = \frac{6 (- (b) - 1 \cdot - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.12.3

Factor $- 1$ out of $- (b) - 1 (- 2)$ .

$8 = \frac{6 (- (b - 2))}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.12.4

Simplify the expression.

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Step 2.3.4.2.1.12.4.1

Rewrite $- (b - 2)$ as $- 1 (b - 2)$ .

$8 = \frac{6 (- 1 (b - 2))}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.2.1.12.4.2

Move the negative in front of the fraction.

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 36 a - 6 b$

Step 2.3.4.3

Replace all occurrences of $a$ in $c = 6 - 36 a - 6 b$ with $- \frac{b}{15} + \frac{2}{15}$ .

$c = 6 - 36 (- \frac{b}{15} + \frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4

Simplify the right side.

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Step 2.3.4.4.1

Simplify $6 - 36 (- \frac{b}{15} + \frac{2}{15}) - 6 b$ .

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Step 2.3.4.4.1.1

Simplify each term.

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Step 2.3.4.4.1.1.1

Apply the distributive property.

$c = 6 - 36 (- \frac{b}{15}) - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.2

Cancel the common factor of $3$ .

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Step 2.3.4.4.1.1.2.1

Move the leading negative in $- \frac{b}{15}$ into the numerator.

$c = 6 - 36 \frac{- b}{15} - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.2.2

Factor $3$ out of $- 36$ .

$c = 6 + 3 (- 12) (\frac{- b}{15}) - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.2.3

Factor $3$ out of $15$ .

$c = 6 + 3 \cdot (- 12 \frac{- b}{3 \cdot 5}) - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.2.4

Cancel the common factor.

$c = 6 + 3 \cdot (- 12 \frac{- b}{3 \cdot 5}) - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.2.5

Rewrite the expression.

$c = 6 - 12 \frac{- b}{5} - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 - 12 \frac{- b}{5} - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.3

Combine $- 12$ and $\frac{- b}{5}$ .

$c = 6 + \frac{- 12 (- b)}{5} - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.4

Multiply $- 1$ by $- 12$ .

$c = 6 + \frac{12 b}{5} - 36 (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.5

Cancel the common factor of $3$ .

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Step 2.3.4.4.1.1.5.1

Factor $3$ out of $- 36$ .

$c = 6 + \frac{12 b}{5} + 3 (- 12) (\frac{2}{15}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.5.2

Factor $3$ out of $15$ .

$c = 6 + \frac{12 b}{5} + 3 \cdot (- 12 \frac{2}{3 \cdot 5}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.5.3

Cancel the common factor.

$c = 6 + \frac{12 b}{5} + 3 \cdot (- 12 \frac{2}{3 \cdot 5}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.5.4

Rewrite the expression.

$c = 6 + \frac{12 b}{5} - 12 (\frac{2}{5}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 + \frac{12 b}{5} - 12 (\frac{2}{5}) - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.6

Combine $- 12$ and $\frac{2}{5}$ .

$c = 6 + \frac{12 b}{5} + \frac{- 12 \cdot 2}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.7

Multiply $- 12$ by $2$ .

$c = 6 + \frac{12 b}{5} + \frac{- 24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.1.8

Move the negative in front of the fraction.

$c = 6 + \frac{12 b}{5} - \frac{24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 6 + \frac{12 b}{5} - \frac{24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$c = \frac{12 b}{5} + 6 \cdot \frac{5}{5} - \frac{24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.3

Combine $6$ and $\frac{5}{5}$ .

$c = \frac{12 b}{5} + \frac{6 \cdot 5}{5} - \frac{24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.4

Combine the numerators over the common denominator.

$c = \frac{12 b}{5} + \frac{6 \cdot 5 - 24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.5

Simplify the numerator.

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Step 2.3.4.4.1.5.1

Multiply $6$ by $5$ .

$c = \frac{12 b}{5} + \frac{30 - 24}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.5.2

Subtract $24$ from $30$ .

$c = \frac{12 b}{5} + \frac{6}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = \frac{12 b}{5} + \frac{6}{5} - 6 b$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.6

To write $- 6 b$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$c = \frac{12 b}{5} - 6 b \cdot \frac{5}{5} + \frac{6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.7

Combine $- 6 b$ and $\frac{5}{5}$ .

$c = \frac{12 b}{5} + \frac{- 6 b \cdot 5}{5} + \frac{6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.8

Combine the numerators over the common denominator.

$c = \frac{12 b - 6 b \cdot 5}{5} + \frac{6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.9

Combine the numerators over the common denominator.

$c = \frac{12 b - 6 b \cdot 5 + 6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.10

Multiply $5$ by $- 6$ .

$c = \frac{12 b - 30 b + 6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.11

Subtract $30 b$ from $12 b$ .

$c = \frac{- 18 b + 6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.12

Factor $6$ out of $- 18 b + 6$ .

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Step 2.3.4.4.1.12.1

Factor $6$ out of $- 18 b$ .

$c = \frac{6 (- 3 b) + 6}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.12.2

Factor $6$ out of $6$ .

$c = \frac{6 (- 3 b) + 6 (1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.12.3

Factor $6$ out of $6 (- 3 b) + 6 (1)$ .

$c = \frac{6 (- 3 b + 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = \frac{6 (- 3 b + 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.13

Factor $- 1$ out of $- 3 b$ .

$c = \frac{6 (- (3 b) + 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.14

Rewrite $1$ as $- 1 (- 1)$ .

$c = \frac{6 (- (3 b) - 1 \cdot - 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.15

Factor $- 1$ out of $- (3 b) - 1 (- 1)$ .

$c = \frac{6 (- (3 b - 1))}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.16

Simplify the expression.

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Step 2.3.4.4.1.16.1

Rewrite $- (3 b - 1)$ as $- 1 (3 b - 1)$ .

$c = \frac{6 (- 1 (3 b - 1))}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.4.4.1.16.2

Move the negative in front of the fraction.

$c = - \frac{6 (3 b - 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = - \frac{6 (3 b - 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = - \frac{6 (3 b - 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = - \frac{6 (3 b - 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = - \frac{6 (3 b - 1)}{5}$

$8 = - \frac{6 (b - 2)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5

Solve for $b$ in $8 = - \frac{6 (b - 2)}{5}$ .

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Step 2.3.5.1

Rewrite the equation as $- \frac{6 (b - 2)}{5} = 8$ .

$- \frac{6 (b - 2)}{5} = 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.2

Multiply both sides of the equation by $- \frac{5}{6}$ .

$- \frac{5}{6} \cdot (- \frac{6 (b - 2)}{5}) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3

Simplify both sides of the equation.

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Step 2.3.5.3.1

Simplify the left side.

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Step 2.3.5.3.1.1

Simplify $- \frac{5}{6} (- \frac{6 (b - 2)}{5})$ .

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Step 2.3.5.3.1.1.1

Cancel the common factor of $5$ .

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Step 2.3.5.3.1.1.1.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{- 5}{6} \cdot (- \frac{6 (b - 2)}{5}) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.1.2

Move the leading negative in $- \frac{6 (b - 2)}{5}$ into the numerator.

$\frac{- 5}{6} \cdot \frac{- 6 (b - 2)}{5} = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{6} \cdot \frac{- 6 (b - 2)}{5} = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{6} \cdot \frac{- 6 (b - 2)}{5} = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{6} \cdot (- 6 (b - 2)) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$\frac{- 1}{6} \cdot (- 6 (b - 2)) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.2

Cancel the common factor of $6$ .

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Step 2.3.5.3.1.1.2.1

Factor $6$ out of $- 6 (b - 2)$ .

$\frac{- 1}{6} \cdot (6 (- (b - 2))) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{6} \cdot (6 (- (b - 2))) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.2.3

Rewrite the expression.

$b - 2 = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.3

Multiply.

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Step 2.3.5.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (b - 2) = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.1.1.3.2

Multiply $b - 2$ by $1$ .

$b - 2 = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2

Simplify the right side.

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Step 2.3.5.3.2.1

Simplify $- \frac{5}{6} \cdot 8$ .

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Step 2.3.5.3.2.1.1

Cancel the common factor of $2$ .

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Step 2.3.5.3.2.1.1.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$b - 2 = \frac{- 5}{6} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.1.2

Factor $2$ out of $6$ .

$b - 2 = \frac{- 5}{2 (3)} \cdot 8$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.1.3

Factor $2$ out of $8$ .

$b - 2 = \frac{- 5}{2 \cdot 3} \cdot (2 \cdot 4)$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.1.4

Cancel the common factor.

$b - 2 = \frac{- 5}{2 \cdot 3} \cdot (2 \cdot 4)$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.1.5

Rewrite the expression.

$b - 2 = \frac{- 5}{3} \cdot 4$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = \frac{- 5}{3} \cdot 4$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.2

Combine $\frac{- 5}{3}$ and $4$ .

$b - 2 = \frac{- 5 \cdot 4}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.3

Simplify the expression.

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Step 2.3.5.3.2.1.3.1

Multiply $- 5$ by $4$ .

$b - 2 = \frac{- 20}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.3.2.1.3.2

Move the negative in front of the fraction.

$b - 2 = - \frac{20}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{20}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{20}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{20}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b - 2 = - \frac{20}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4

Move all terms not containing $b$ to the right side of the equation.

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Step 2.3.5.4.1

Add $2$ to both sides of the equation.

$b = - \frac{20}{3} + 2$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - \frac{20}{3} + 2 \cdot \frac{3}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4.3

Combine $2$ and $\frac{3}{3}$ .

$b = - \frac{20}{3} + \frac{2 \cdot 3}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4.4

Combine the numerators over the common denominator.

$b = \frac{- 20 + 2 \cdot 3}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4.5

Simplify the numerator.

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Step 2.3.5.4.5.1

Multiply $2$ by $3$ .

$b = \frac{- 20 + 6}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4.5.2

Add $- 20$ and $6$ .

$b = \frac{- 14}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b = \frac{- 14}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.5.4.6

Move the negative in front of the fraction.

$b = - \frac{14}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b = - \frac{14}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

$b = - \frac{14}{3}$

$c = - \frac{6 (3 b - 1)}{5}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6

Replace all occurrences of $b$ with $- \frac{14}{3}$ in each equation.

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Step 2.3.6.1

Replace all occurrences of $b$ in $c = - \frac{6 (3 b - 1)}{5}$ with $- \frac{14}{3}$ .

$c = - \frac{6 (3 (- \frac{14}{3}) - 1)}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2

Simplify the right side.

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Step 2.3.6.2.1

Simplify $- \frac{6 (3 (- \frac{14}{3}) - 1)}{5}$ .

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Step 2.3.6.2.1.1

Simplify the numerator.

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Step 2.3.6.2.1.1.1

Cancel the common factor of $3$ .

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Step 2.3.6.2.1.1.1.1

Move the leading negative in $- \frac{14}{3}$ into the numerator.

$c = - \frac{6 (3 (\frac{- 14}{3}) - 1)}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2.1.1.1.2

Cancel the common factor.

$c = - \frac{6 (3 (\frac{- 14}{3}) - 1)}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2.1.1.1.3

Rewrite the expression.

$c = - \frac{6 (- 14 - 1)}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = - \frac{6 (- 14 - 1)}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2.1.1.2

Subtract $1$ from $- 14$ .

$c = - \frac{6 \cdot - 15}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = - \frac{6 \cdot - 15}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2.1.2

Simplify the expression.

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Step 2.3.6.2.1.2.1

Multiply $6$ by $- 15$ .

$c = - \frac{- 90}{5}$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2.1.2.2

Divide $- 90$ by $5$ .

$c = 18$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.2.1.2.3

Multiply $- 1$ by $- 18$ .

$c = 18$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 18$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 18$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

$c = 18$

$b = - \frac{14}{3}$

$a = - \frac{b}{15} + \frac{2}{15}$

Step 2.3.6.3

Replace all occurrences of $b$ in $a = - \frac{b}{15} + \frac{2}{15}$ with $- \frac{14}{3}$ .

$a = - \frac{- \frac{14}{3}}{15} + \frac{2}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4

Simplify the right side.

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Step 2.3.6.4.1

Simplify $- \frac{- \frac{14}{3}}{15} + \frac{2}{15}$ .

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Step 2.3.6.4.1.1

Combine the numerators over the common denominator.

$a = \frac{\frac{14}{3} + 2}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$a = \frac{\frac{14}{3} + 2 \cdot \frac{3}{3}}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.3

Combine $2$ and $\frac{3}{3}$ .

$a = \frac{\frac{14}{3} + \frac{2 \cdot 3}{3}}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.4

Combine the numerators over the common denominator.

$a = \frac{\frac{14 + 2 \cdot 3}{3}}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.5

Simplify the numerator.

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Step 2.3.6.4.1.5.1

Multiply $2$ by $3$ .

$a = \frac{\frac{14 + 6}{3}}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.5.2

Add $14$ and $6$ .

$a = \frac{\frac{20}{3}}{15}$

$c = 18$

$b = - \frac{14}{3}$

$a = \frac{\frac{20}{3}}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.6

Multiply the numerator by the reciprocal of the denominator.

$a = \frac{20}{3} \cdot \frac{1}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.7

Cancel the common factor of $5$ .

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Step 2.3.6.4.1.7.1

Factor $5$ out of $20$ .

$a = \frac{5 (4)}{3} \cdot \frac{1}{15}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.7.2

Factor $5$ out of $15$ .

$a = \frac{5 \cdot 4}{3} \cdot \frac{1}{5 \cdot 3}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.7.3

Cancel the common factor.

$a = \frac{5 \cdot 4}{3} \cdot \frac{1}{5 \cdot 3}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.7.4

Rewrite the expression.

$a = \frac{4}{3} \cdot \frac{1}{3}$

$c = 18$

$b = - \frac{14}{3}$

$a = \frac{4}{3} \cdot \frac{1}{3}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.8

Multiply $\frac{4}{3}$ by $\frac{1}{3}$ .

$a = \frac{4}{3 \cdot 3}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.6.4.1.9

Multiply $3$ by $3$ .

$a = \frac{4}{9}$

$c = 18$

$b = - \frac{14}{3}$

$a = \frac{4}{9}$

$c = 18$

$b = - \frac{14}{3}$

$a = \frac{4}{9}$

$c = 18$

$b = - \frac{14}{3}$

$a = \frac{4}{9}$

$c = 18$

$b = - \frac{14}{3}$

Step 2.3.7

List all of the solutions.

$a = \frac{4}{9}, c = 18, b = - \frac{14}{3}$

Step 2.4

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

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Step 2.4.1

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = \frac{4}{9}$ , $b = - \frac{14}{3}$ , $c = 18$ , and $x = 6$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Raise $6$ to the power of $2$ .

$y = \frac{4}{9} \cdot 36 + (- \frac{14}{3}) \cdot (6) + 18$

Step 2.4.1.1.2

Cancel the common factor of $9$ .

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Step 2.4.1.1.2.1

Factor $9$ out of $36$ .

$y = \frac{4}{9} \cdot (9 (4)) + (- \frac{14}{3}) \cdot (6) + 18$

Step 2.4.1.1.2.2

Cancel the common factor.

$y = \frac{4}{9} \cdot (9 \cdot 4) + (- \frac{14}{3}) \cdot (6) + 18$

Step 2.4.1.1.2.3

Rewrite the expression.

$y = 4 \cdot 4 + (- \frac{14}{3}) \cdot (6) + 18$

Step 2.4.1.1.3

Multiply $4$ by $4$ .

$y = 16 + (- \frac{14}{3}) \cdot (6) + 18$

Step 2.4.1.1.4

Cancel the common factor of $3$ .

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Step 2.4.1.1.4.1

Move the leading negative in $- \frac{14}{3}$ into the numerator.

$y = 16 + \frac{- 14}{3} \cdot 6 + 18$

Step 2.4.1.1.4.2

Factor $3$ out of $6$ .

$y = 16 + \frac{- 14}{3} \cdot (3 (2)) + 18$

Step 2.4.1.1.4.3

Cancel the common factor.

$y = 16 + \frac{- 14}{3} \cdot (3 \cdot 2) + 18$

Step 2.4.1.1.4.4

Rewrite the expression.

$y = 16 - 14 \cdot 2 + 18$

Step 2.4.1.1.5

Multiply $- 14$ by $2$ .

$y = 16 - 28 + 18$

Step 2.4.1.2

Simplify by adding and subtracting.

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Step 2.4.1.2.1

Subtract $28$ from $16$ .

$y = - 12 + 18$

Step 2.4.1.2.2

Add $- 12$ and $18$ .

$y = 6$

Step 2.4.2

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 6$ . This check passes since $y = 6$ and $y = 6$ .

$6 = 6$

Step 2.4.3

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = \frac{4}{9}$ , $b = - \frac{14}{3}$ , $c = 18$ , and $x = 3$ .

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Step 2.4.3.1

Simplify each term.

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Step 2.4.3.1.1

Raise $3$ to the power of $2$ .

$y = \frac{4}{9} \cdot 9 + (- \frac{14}{3}) \cdot (3) + 18$

Step 2.4.3.1.2

Cancel the common factor of $9$ .

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Step 2.4.3.1.2.1

Cancel the common factor.

$y = \frac{4}{9} \cdot 9 + (- \frac{14}{3}) \cdot (3) + 18$

Step 2.4.3.1.2.2

Rewrite the expression.

$y = 4 + (- \frac{14}{3}) \cdot (3) + 18$

Step 2.4.3.1.3

Cancel the common factor of $3$ .

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Step 2.4.3.1.3.1

Move the leading negative in $- \frac{14}{3}$ into the numerator.

$y = 4 + \frac{- 14}{3} \cdot 3 + 18$

Step 2.4.3.1.3.2

Cancel the common factor.

$y = 4 + \frac{- 14}{3} \cdot 3 + 18$

Step 2.4.3.1.3.3

Rewrite the expression.

$y = 4 - 14 + 18$

Step 2.4.3.2

Simplify by adding and subtracting.

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Step 2.4.3.2.1

Subtract $14$ from $4$ .

$y = - 10 + 18$

Step 2.4.3.2.2

Add $- 10$ and $18$ .

$y = 8$

Step 2.4.4

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 3$ . This check passes since $y = 8$ and $y = 8$ .

$8 = 8$

Step 2.4.5

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = \frac{4}{9}$ , $b = - \frac{14}{3}$ , $c = 18$ , and $x = 9$ .

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Step 2.4.5.1

Simplify each term.

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Step 2.4.5.1.1

Cancel the common factor of $9$ .

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Step 2.4.5.1.1.1

Factor $9$ out of ${(9)}^{2}$ .

$y = \frac{4}{9} \cdot (9 \cdot 9) + (- \frac{14}{3}) \cdot (9) + 18$

Step 2.4.5.1.1.2

Cancel the common factor.

$y = \frac{4}{9} \cdot (9 \cdot 9) + (- \frac{14}{3}) \cdot (9) + 18$

Step 2.4.5.1.1.3

Rewrite the expression.

$y = 4 \cdot 9 + (- \frac{14}{3}) \cdot (9) + 18$

Step 2.4.5.1.2

Multiply $4$ by $9$ .

$y = 36 + (- \frac{14}{3}) \cdot (9) + 18$

Step 2.4.5.1.3

Cancel the common factor of $3$ .

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Step 2.4.5.1.3.1

Move the leading negative in $- \frac{14}{3}$ into the numerator.

$y = 36 + \frac{- 14}{3} \cdot 9 + 18$

Step 2.4.5.1.3.2

Factor $3$ out of $9$ .

$y = 36 + \frac{- 14}{3} \cdot (3 (3)) + 18$

Step 2.4.5.1.3.3

Cancel the common factor.

$y = 36 + \frac{- 14}{3} \cdot (3 \cdot 3) + 18$

Step 2.4.5.1.3.4

Rewrite the expression.

$y = 36 - 14 \cdot 3 + 18$

Step 2.4.5.1.4

Multiply $- 14$ by $3$ .

$y = 36 - 42 + 18$

Step 2.4.5.2

Simplify by adding and subtracting.

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Step 2.4.5.2.1

Subtract $42$ from $36$ .

$y = - 6 + 18$

Step 2.4.5.2.2

Add $- 6$ and $18$ .

$y = 12$

Step 2.4.6

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 9$ . This check passes since $y = 12$ and $y = 12$ .

$12 = 12$

Step 2.4.7

Since $y = y$ for the corresponding $x$ values, the function is quadratic.

The function is quadratic

Step 3

Since all $y = y$ , the function is quadratic and follows the form $y = \frac{4 x^{2}}{9} - \frac{14 x}{3} + 18$ .

$y = \frac{4 x^{2}}{9} - \frac{14 x}{3} + 18$