Algebra Examples

$\begin{array}{c} x & y \\ 2 & 860 \\ 4 & 1250 \\ 6 & 1800 \end{array}$

Step 1

Check if the function rule is linear.

Tap for more steps...

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 $y = a x + b$ .

$860 = a (2) + b 1250 = a (4) + b 1800 = a (6) + b$

Step 1.3

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

Tap for more steps...

Step 1.3.1

Solve for $b$ in $860 = a (2) + b$ .

Tap for more steps...

Step 1.3.1.1

Rewrite the equation as $a (2) + b = 860$ .

$a (2) + b = 860$

$1250 = a (4) + b$

$1800 = a (6) + b$

Step 1.3.1.2

Move $2$ to the left of $a$ .

$2 a + b = 860$

$1250 = a (4) + b$

$1800 = a (6) + b$

Step 1.3.1.3

Subtract $2 a$ from both sides of the equation.

$b = 860 - 2 a$

$1250 = a (4) + b$

$1800 = a (6) + b$

$b = 860 - 2 a$

$1250 = a (4) + b$

$1800 = a (6) + b$

Step 1.3.2

Replace all occurrences of $b$ with $860 - 2 a$ in each equation.

Tap for more steps...

Step 1.3.2.1

Replace all occurrences of $b$ in $1250 = a (4) + b$ with $860 - 2 a$ .

$1250 = a (4) + 860 - 2 a$

$b = 860 - 2 a$

$1800 = a (6) + b$

Step 1.3.2.2

Simplify $1250 = a (4) + 860 - 2 a$ .

Tap for more steps...

Step 1.3.2.2.1

Simplify the left side.

Tap for more steps...

Step 1.3.2.2.1.1

Remove parentheses.

$1250 = a (4) + 860 - 2 a$

$b = 860 - 2 a$

$1800 = a (6) + b$

$1250 = a (4) + 860 - 2 a$

$b = 860 - 2 a$

$1800 = a (6) + b$

Step 1.3.2.2.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.2.2.1

Simplify $a (4) + 860 - 2 a$ .

Tap for more steps...

Step 1.3.2.2.2.1.1

Move $4$ to the left of $a$ .

$1250 = 4 a + 860 - 2 a$

$b = 860 - 2 a$

$1800 = a (6) + b$

Step 1.3.2.2.2.1.2

Subtract $2 a$ from $4 a$ .

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = a (6) + b$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = a (6) + b$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = a (6) + b$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = a (6) + b$

Step 1.3.2.3

Replace all occurrences of $b$ in $1800 = a (6) + b$ with $860 - 2 a$ .

$1800 = a (6) + 860 - 2 a$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.2.4

Simplify $1800 = a (6) + 860 - 2 a$ .

Tap for more steps...

Step 1.3.2.4.1

Simplify the left side.

Tap for more steps...

Step 1.3.2.4.1.1

Remove parentheses.

$1800 = a (6) + 860 - 2 a$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = a (6) + 860 - 2 a$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.2.4.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.4.2.1

Simplify $a (6) + 860 - 2 a$ .

Tap for more steps...

Step 1.3.2.4.2.1.1

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

$1800 = 6 a + 860 - 2 a$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.2.4.2.1.2

Subtract $2 a$ from $6 a$ .

$1800 = 4 a + 860$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = 4 a + 860$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = 4 a + 860$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = 4 a + 860$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$1800 = 4 a + 860$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3

Solve for $a$ in $1800 = 4 a + 860$ .

Tap for more steps...

Step 1.3.3.1

Rewrite the equation as $4 a + 860 = 1800$ .

$4 a + 860 = 1800$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3.2

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

Tap for more steps...

Step 1.3.3.2.1

Subtract $860$ from both sides of the equation.

$4 a = 1800 - 860$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3.2.2

Subtract $860$ from $1800$ .

$4 a = 940$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$4 a = 940$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3.3

Divide each term in $4 a = 940$ by $4$ and simplify.

Tap for more steps...

Step 1.3.3.3.1

Divide each term in $4 a = 940$ by $4$ .

$\frac{4 a}{4} = \frac{940}{4}$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.3.3.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 1.3.3.3.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{940}{4}$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{940}{4}$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$a = \frac{940}{4}$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$a = \frac{940}{4}$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.3.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.3.3.1

Divide $940$ by $4$ .

$a = 235$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$a = 235$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$a = 235$

$1250 = 2 a + 860$

$b = 860 - 2 a$

$a = 235$

$1250 = 2 a + 860$

$b = 860 - 2 a$

Step 1.3.4

Replace all occurrences of $a$ with $235$ in each equation.

Tap for more steps...

Step 1.3.4.1

Replace all occurrences of $a$ in $1250 = 2 a + 860$ with $235$ .

$1250 = 2 (235) + 860$

$a = 235$

$b = 860 - 2 a$

Step 1.3.4.2

Simplify the right side.

Tap for more steps...

Step 1.3.4.2.1

Simplify $2 (235) + 860$ .

Tap for more steps...

Step 1.3.4.2.1.1

Multiply $2$ by $235$ .

$1250 = 470 + 860$

$a = 235$

$b = 860 - 2 a$

Step 1.3.4.2.1.2

Add $470$ and $860$ .

$1250 = 1330$

$a = 235$

$b = 860 - 2 a$

$1250 = 1330$

$a = 235$

$b = 860 - 2 a$

$1250 = 1330$

$a = 235$

$b = 860 - 2 a$

Step 1.3.4.3

Replace all occurrences of $a$ in $b = 860 - 2 a$ with $235$ .

$b = 860 - 2 \cdot 235$

$1250 = 1330$

$a = 235$

Step 1.3.4.4

Simplify the right side.

Tap for more steps...

Step 1.3.4.4.1

Simplify $860 - 2 \cdot 235$ .

Tap for more steps...

Step 1.3.4.4.1.1

Multiply $- 2$ by $235$ .

$b = 860 - 470$

$1250 = 1330$

$a = 235$

Step 1.3.4.4.1.2

Subtract $470$ from $860$ .

$b = 390$

$1250 = 1330$

$a = 235$

$b = 390$

$1250 = 1330$

$a = 235$

$b = 390$

$1250 = 1330$

$a = 235$

$b = 390$

$1250 = 1330$

$a = 235$

Step 1.3.5

Since $1250 = 1330$ 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.

Tap for more steps...

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 $c$ .

Tap for more steps...

Step 2.3.1

Solve for $c$ in $860 = a \cdot 2^{2} + b (2) + c$ .

Tap for more steps...

Step 2.3.1.1

Rewrite the equation as $a \cdot 2^{2} + b (2) + c = 860$ .

$a \cdot 2^{2} + b (2) + c = 860$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.1.2

Simplify each term.

Tap for more steps...

Step 2.3.1.2.1

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

$a \cdot 4 + b (2) + c = 860$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.1.2.2

Move $4$ to the left of $a$ .

$4 \cdot a + b (2) + c = 860$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.1.2.3

Move $2$ to the left of $b$ .

$4 a + 2 b + c = 860$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

$4 a + 2 b + c = 860$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.1.3

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

Tap for more steps...

Step 2.3.1.3.1

Subtract $4 a$ from both sides of the equation.

$2 b + c = 860 - 4 a$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.1.3.2

Subtract $2 b$ from both sides of the equation.

$c = 860 - 4 a - 2 b$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

$c = 860 - 4 a - 2 b$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

$c = 860 - 4 a - 2 b$

$1250 = a \cdot 4^{2} + b (4) + c$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2

Replace all occurrences of $c$ with $860 - 4 a - 2 b$ in each equation.

Tap for more steps...

Step 2.3.2.1

Replace all occurrences of $c$ in $1250 = a \cdot 4^{2} + b (4) + c$ with $860 - 4 a - 2 b$ .

$1250 = a \cdot 4^{2} + b (4) + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.2

Simplify $1250 = a \cdot 4^{2} + b (4) + 860 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.2.1

Simplify the left side.

Tap for more steps...

Step 2.3.2.2.1.1

Remove parentheses.

$1250 = a \cdot 4^{2} + b (4) + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

$1250 = a \cdot 4^{2} + b (4) + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.2.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.2.2.1

Simplify $a \cdot 4^{2} + b (4) + 860 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.2.2.2.1.1.1

Raise $4$ to the power of $2$ .

$1250 = a \cdot 16 + b (4) + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.2.2.1.1.2

Move $16$ to the left of $a$ .

$1250 = 16 \cdot a + b (4) + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.2.2.1.1.3

Move $4$ to the left of $b$ .

$1250 = 16 a + 4 b + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

$1250 = 16 a + 4 b + 860 - 4 a - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.3.2.2.2.1.2.1

Subtract $4 a$ from $16 a$ .

$1250 = 12 a + 4 b + 860 - 2 b$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.2.2.1.2.2

Subtract $2 b$ from $4 b$ .

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + c$

Step 2.3.2.3

Replace all occurrences of $c$ in $1800 = a \cdot 6^{2} + b (6) + c$ with $860 - 4 a - 2 b$ .

$1800 = a \cdot 6^{2} + b (6) + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.2.4

Simplify $1800 = a \cdot 6^{2} + b (6) + 860 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.4.1

Simplify the left side.

Tap for more steps...

Step 2.3.2.4.1.1

Remove parentheses.

$1800 = a \cdot 6^{2} + b (6) + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = a \cdot 6^{2} + b (6) + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.2.4.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.4.2.1

Simplify $a \cdot 6^{2} + b (6) + 860 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.4.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.2.4.2.1.1.1

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

$1800 = a \cdot 36 + b (6) + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.2.4.2.1.1.2

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

$1800 = 36 \cdot a + b (6) + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.2.4.2.1.1.3

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

$1800 = 36 a + 6 b + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = 36 a + 6 b + 860 - 4 a - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.2.4.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.3.2.4.2.1.2.1

Subtract $4 a$ from $36 a$ .

$1800 = 32 a + 6 b + 860 - 2 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.2.4.2.1.2.2

Subtract $2 b$ from $6 b$ .

$1800 = 32 a + 4 b + 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = 32 a + 4 b + 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = 32 a + 4 b + 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = 32 a + 4 b + 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = 32 a + 4 b + 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$1800 = 32 a + 4 b + 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3

Solve for $a$ in $1800 = 32 a + 4 b + 860$ .

Tap for more steps...

Step 2.3.3.1

Rewrite the equation as $32 a + 4 b + 860 = 1800$ .

$32 a + 4 b + 860 = 1800$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.2

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

Tap for more steps...

Step 2.3.3.2.1

Subtract $4 b$ from both sides of the equation.

$32 a + 860 = 1800 - 4 b$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.2.2

Subtract $860$ from both sides of the equation.

$32 a = 1800 - 4 b - 860$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.2.3

Subtract $860$ from $1800$ .

$32 a = - 4 b + 940$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$32 a = - 4 b + 940$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3

Divide each term in $32 a = - 4 b + 940$ by $32$ and simplify.

Tap for more steps...

Step 2.3.3.3.1

Divide each term in $32 a = - 4 b + 940$ by $32$ .

$\frac{32 a}{32} = \frac{- 4 b}{32} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.3.3.2.1

Cancel the common factor of $32$ .

Tap for more steps...

Step 2.3.3.3.2.1.1

Cancel the common factor.

$\frac{32 a}{32} = \frac{- 4 b}{32} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 4 b}{32} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = \frac{- 4 b}{32} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = \frac{- 4 b}{32} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.3.3.1

Simplify each term.

Tap for more steps...

Step 2.3.3.3.3.1.1

Cancel the common factor of $- 4$ and $32$ .

Tap for more steps...

Step 2.3.3.3.3.1.1.1

Factor $4$ out of $- 4 b$ .

$a = \frac{4 (- b)}{32} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.3.3.3.1.1.2.1

Factor $4$ out of $32$ .

$a = \frac{4 (- b)}{4 (8)} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.1.2.2

Cancel the common factor.

$a = \frac{4 (- b)}{4 \cdot 8} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.1.2.3

Rewrite the expression.

$a = \frac{- b}{8} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = \frac{- b}{8} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = \frac{- b}{8} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.2

Move the negative in front of the fraction.

$a = - \frac{b}{8} + \frac{940}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.3

Cancel the common factor of $940$ and $32$ .

Tap for more steps...

Step 2.3.3.3.3.1.3.1

Factor $4$ out of $940$ .

$a = - \frac{b}{8} + \frac{4 (235)}{32}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.3.3.3.1.3.2.1

Factor $4$ out of $32$ .

$a = - \frac{b}{8} + \frac{4 \cdot 235}{4 \cdot 8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.3.2.2

Cancel the common factor.

$a = - \frac{b}{8} + \frac{4 \cdot 235}{4 \cdot 8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.3.3.3.1.3.2.3

Rewrite the expression.

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

$a = - \frac{b}{8} + \frac{235}{8}$

$1250 = 12 a + 2 b + 860$

$c = 860 - 4 a - 2 b$

Step 2.3.4

Replace all occurrences of $a$ with $- \frac{b}{8} + \frac{235}{8}$ in each equation.

Tap for more steps...

Step 2.3.4.1

Replace all occurrences of $a$ in $1250 = 12 a + 2 b + 860$ with $- \frac{b}{8} + \frac{235}{8}$ .

$1250 = 12 (- \frac{b}{8} + \frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2

Simplify the right side.

Tap for more steps...

Step 2.3.4.2.1

Simplify $12 (- \frac{b}{8} + \frac{235}{8}) + 2 b + 860$ .

Tap for more steps...

Step 2.3.4.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.4.2.1.1.1

Apply the distributive property.

$1250 = 12 (- \frac{b}{8}) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.2.1.1.2.1

Move the leading negative in $- \frac{b}{8}$ into the numerator.

$1250 = 12 (\frac{- b}{8}) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.2

Factor $4$ out of $12$ .

$1250 = 4 (3) (\frac{- b}{8}) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.3

Factor $4$ out of $8$ .

$1250 = 4 \cdot (3 (\frac{- b}{4 \cdot 2})) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.4

Cancel the common factor.

$1250 = 4 \cdot (3 (\frac{- b}{4 \cdot 2})) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.5

Rewrite the expression.

$1250 = 3 (\frac{- b}{2}) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = 3 (\frac{- b}{2}) + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.3

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

$1250 = \frac{3 (- b)}{2} + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.4

Multiply $- 1$ by $3$ .

$1250 = \frac{- 3 b}{2} + 12 (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.5

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.2.1.1.5.1

Factor $4$ out of $12$ .

$1250 = \frac{- 3 b}{2} + 4 (3) (\frac{235}{8}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.5.2

Factor $4$ out of $8$ .

$1250 = \frac{- 3 b}{2} + 4 \cdot (3 (\frac{235}{4 \cdot 2})) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.5.3

Cancel the common factor.

$1250 = \frac{- 3 b}{2} + 4 \cdot (3 (\frac{235}{4 \cdot 2})) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.5.4

Rewrite the expression.

$1250 = \frac{- 3 b}{2} + 3 (\frac{235}{2}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = \frac{- 3 b}{2} + 3 (\frac{235}{2}) + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.6

Combine $3$ and $\frac{235}{2}$ .

$1250 = \frac{- 3 b}{2} + \frac{3 \cdot 235}{2} + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.7

Multiply $3$ by $235$ .

$1250 = \frac{- 3 b}{2} + \frac{705}{2} + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.1.8

Move the negative in front of the fraction.

$1250 = - \frac{3 b}{2} + \frac{705}{2} + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = - \frac{3 b}{2} + \frac{705}{2} + 2 b + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.2

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

$1250 = - \frac{3 b}{2} + 2 b \cdot \frac{2}{2} + \frac{705}{2} + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.3

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

$1250 = - \frac{3 b}{2} + \frac{2 b \cdot 2}{2} + \frac{705}{2} + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.4

Combine the numerators over the common denominator.

$1250 = \frac{- 3 b + 2 b \cdot 2}{2} + \frac{705}{2} + 860$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.5

Combine the numerators over the common denominator.

$1250 = 860 + \frac{- 3 b + 2 b \cdot 2 + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.6

Multiply $2$ by $2$ .

$1250 = 860 + \frac{- 3 b + 4 b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.7

Add $- 3 b$ and $4 b$ .

$1250 = 860 + \frac{b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.8

To write $860$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$1250 = 860 \cdot \frac{2}{2} + \frac{b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.9

Simplify terms.

Tap for more steps...

Step 2.3.4.2.1.9.1

Combine $860$ and $\frac{2}{2}$ .

$1250 = \frac{860 \cdot 2}{2} + \frac{b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.9.2

Combine the numerators over the common denominator.

$1250 = \frac{860 \cdot 2 + b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = \frac{860 \cdot 2 + b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.10

Simplify the numerator.

Tap for more steps...

Step 2.3.4.2.1.10.1

Multiply $860$ by $2$ .

$1250 = \frac{1720 + b + 705}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.2.1.10.2

Add $1720$ and $705$ .

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 4 a - 2 b$

Step 2.3.4.3

Replace all occurrences of $a$ in $c = 860 - 4 a - 2 b$ with $- \frac{b}{8} + \frac{235}{8}$ .

$c = 860 - 4 (- \frac{b}{8} + \frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4

Simplify the right side.

Tap for more steps...

Step 2.3.4.4.1

Simplify $860 - 4 (- \frac{b}{8} + \frac{235}{8}) - 2 b$ .

Tap for more steps...

Step 2.3.4.4.1.1

Simplify each term.

Tap for more steps...

Step 2.3.4.4.1.1.1

Apply the distributive property.

$c = 860 - 4 (- \frac{b}{8}) - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.4.1.1.2.1

Move the leading negative in $- \frac{b}{8}$ into the numerator.

$c = 860 - 4 \frac{- b}{8} - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.2.2

Factor $4$ out of $- 4$ .

$c = 860 + 4 (- 1) (\frac{- b}{8}) - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.2.3

Factor $4$ out of $8$ .

$c = 860 + 4 \cdot (- 1 \frac{- b}{4 \cdot 2}) - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.2.4

Cancel the common factor.

$c = 860 + 4 \cdot (- 1 \frac{- b}{4 \cdot 2}) - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.2.5

Rewrite the expression.

$c = 860 - 1 \frac{- b}{2} - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 1 \frac{- b}{2} - 4 (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.4.1.1.3.1

Factor $4$ out of $- 4$ .

$c = 860 - 1 \frac{- b}{2} + 4 (- 1) (\frac{235}{8}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.3.2

Factor $4$ out of $8$ .

$c = 860 - 1 \frac{- b}{2} + 4 \cdot (- 1 \frac{235}{4 \cdot 2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.3.3

Cancel the common factor.

$c = 860 - 1 \frac{- b}{2} + 4 \cdot (- 1 \frac{235}{4 \cdot 2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.3.4

Rewrite the expression.

$c = 860 - 1 \frac{- b}{2} - 1 (\frac{235}{2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 - 1 \frac{- b}{2} - 1 (\frac{235}{2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.4

Simplify each term.

Tap for more steps...

Step 2.3.4.4.1.1.4.1

Move the negative in front of the fraction.

$c = 860 - 1 (- \frac{b}{2}) - 1 (\frac{235}{2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.4.2

Multiply $- 1 (- \frac{b}{2})$ .

Tap for more steps...

Step 2.3.4.4.1.1.4.2.1

Multiply $- 1$ by $- 1$ .

$c = 860 + 1 (\frac{b}{2}) - 1 (\frac{235}{2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.4.2.2

Multiply $\frac{b}{2}$ by $1$ .

$c = 860 + \frac{b}{2} - 1 (\frac{235}{2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 + \frac{b}{2} - 1 (\frac{235}{2}) - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.1.4.3

Rewrite $- 1 (\frac{235}{2})$ as $- (\frac{235}{2})$ .

$c = 860 + \frac{b}{2} - \frac{235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 + \frac{b}{2} - \frac{235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 860 + \frac{b}{2} - \frac{235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.2

To write $860$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$c = \frac{b}{2} + 860 \cdot \frac{2}{2} - \frac{235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.3

Combine $860$ and $\frac{2}{2}$ .

$c = \frac{b}{2} + \frac{860 \cdot 2}{2} - \frac{235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.4

Combine the numerators over the common denominator.

$c = \frac{b}{2} + \frac{860 \cdot 2 - 235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.5

Simplify the numerator.

Tap for more steps...

Step 2.3.4.4.1.5.1

Multiply $860$ by $2$ .

$c = \frac{b}{2} + \frac{1720 - 235}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.5.2

Subtract $235$ from $1720$ .

$c = \frac{b}{2} + \frac{1485}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = \frac{b}{2} + \frac{1485}{2} - 2 b$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.6

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

$c = \frac{b}{2} - 2 b \cdot \frac{2}{2} + \frac{1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.7

Combine $- 2 b$ and $\frac{2}{2}$ .

$c = \frac{b}{2} + \frac{- 2 b \cdot 2}{2} + \frac{1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.8

Combine the numerators over the common denominator.

$c = \frac{b - 2 b \cdot 2}{2} + \frac{1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.9

Combine the numerators over the common denominator.

$c = \frac{b - 2 b \cdot 2 + 1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.10

Multiply $2$ by $- 2$ .

$c = \frac{b - 4 b + 1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.11

Subtract $4 b$ from $b$ .

$c = \frac{- 3 b + 1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.12

Factor $3$ out of $- 3 b + 1485$ .

Tap for more steps...

Step 2.3.4.4.1.12.1

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

$c = \frac{3 (- b) + 1485}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.12.2

Factor $3$ out of $1485$ .

$c = \frac{3 (- b) + 3 (495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.12.3

Factor $3$ out of $3 (- b) + 3 (495)$ .

$c = \frac{3 (- b + 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = \frac{3 (- b + 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.13

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

$c = \frac{3 (- (b) + 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.14

Rewrite $495$ as $- 1 (- 495)$ .

$c = \frac{3 (- (b) - 1 \cdot - 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.15

Factor $- 1$ out of $- (b) - 1 (- 495)$ .

$c = \frac{3 (- (b - 495))}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.16

Simplify the expression.

Tap for more steps...

Step 2.3.4.4.1.16.1

Rewrite $- (b - 495)$ as $- 1 (b - 495)$ .

$c = \frac{3 (- 1 (b - 495))}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.4.4.1.16.2

Move the negative in front of the fraction.

$c = - \frac{3 (b - 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = - \frac{3 (b - 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = - \frac{3 (b - 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = - \frac{3 (b - 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = - \frac{3 (b - 495)}{2}$

$1250 = \frac{b + 2425}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5

Solve for $b$ in $1250 = \frac{b + 2425}{2}$ .

Tap for more steps...

Step 2.3.5.1

Rewrite the equation as $\frac{b + 2425}{2} = 1250$ .

$\frac{b + 2425}{2} = 1250$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5.2

Multiply both sides of the equation by $2$ .

$2 (\frac{b + 2425}{2}) = 2 \cdot 1250$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5.3

Simplify both sides of the equation.

Tap for more steps...

Step 2.3.5.3.1

Simplify the left side.

Tap for more steps...

Step 2.3.5.3.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.5.3.1.1.1

Cancel the common factor.

$2 (\frac{b + 2425}{2}) = 2 \cdot 1250$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5.3.1.1.2

Rewrite the expression.

$b + 2425 = 2 \cdot 1250$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$b + 2425 = 2 \cdot 1250$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$b + 2425 = 2 \cdot 1250$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5.3.2

Simplify the right side.

Tap for more steps...

Step 2.3.5.3.2.1

Multiply $2$ by $1250$ .

$b + 2425 = 2500$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$b + 2425 = 2500$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$b + 2425 = 2500$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5.4

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

Tap for more steps...

Step 2.3.5.4.1

Subtract $2425$ from both sides of the equation.

$b = 2500 - 2425$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.5.4.2

Subtract $2425$ from $2500$ .

$b = 75$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$b = 75$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

$b = 75$

$c = - \frac{3 (b - 495)}{2}$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.6

Replace all occurrences of $b$ with $75$ in each equation.

Tap for more steps...

Step 2.3.6.1

Replace all occurrences of $b$ in $c = - \frac{3 (b - 495)}{2}$ with $75$ .

$c = - \frac{3 ((75) - 495)}{2}$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.6.2

Simplify the right side.

Tap for more steps...

Step 2.3.6.2.1

Simplify $- \frac{3 ((75) - 495)}{2}$ .

Tap for more steps...

Step 2.3.6.2.1.1

Subtract $495$ from $75$ .

$c = - \frac{3 \cdot - 420}{2}$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.6.2.1.2

Multiply $3$ by $- 420$ .

$c = - \frac{- 1260}{2}$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.6.2.1.3

Divide $- 1260$ by $2$ .

$c = 630$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.6.2.1.4

Multiply $- 1$ by $- 630$ .

$c = 630$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 630$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

$c = 630$

$b = 75$

$a = - \frac{b}{8} + \frac{235}{8}$

Step 2.3.6.3

Replace all occurrences of $b$ in $a = - \frac{b}{8} + \frac{235}{8}$ with $75$ .

$a = - \frac{75}{8} + \frac{235}{8}$

$c = 630$

$b = 75$

Step 2.3.6.4

Simplify the right side.

Tap for more steps...

Step 2.3.6.4.1

Simplify $- \frac{75}{8} + \frac{235}{8}$ .

Tap for more steps...

Step 2.3.6.4.1.1

Combine the numerators over the common denominator.

$a = \frac{- 75 + 235}{8}$

$c = 630$

$b = 75$

Step 2.3.6.4.1.2

Simplify the expression.

Tap for more steps...

Step 2.3.6.4.1.2.1

Add $- 75$ and $235$ .

$a = \frac{160}{8}$

$c = 630$

$b = 75$

Step 2.3.6.4.1.2.2

Divide $160$ by $8$ .

$a = 20$

$c = 630$

$b = 75$

$a = 20$

$c = 630$

$b = 75$

$a = 20$

$c = 630$

$b = 75$

$a = 20$

$c = 630$

$b = 75$

$a = 20$

$c = 630$

$b = 75$

Step 2.3.7

List all of the solutions.

$a = 20, c = 630, b = 75$

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.

Tap for more steps...

Step 2.4.1

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = 20$ , $b = 75$ , $c = 630$ , and $x = 2$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

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

$y = 20 \cdot 4 + (75) \cdot (2) + 630$

Step 2.4.1.1.2

Multiply $20$ by $4$ .

$y = 80 + (75) \cdot (2) + 630$

Step 2.4.1.1.3

Multiply $75$ by $2$ .

$y = 80 + 150 + 630$

Step 2.4.1.2

Simplify by adding numbers.

Tap for more steps...

Step 2.4.1.2.1

Add $80$ and $150$ .

$y = 230 + 630$

Step 2.4.1.2.2

Add $230$ and $630$ .

$y = 860$

Step 2.4.2

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check passes since $y = 860$ and $y = 860$ .

$860 = 860$

Step 2.4.3

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = 20$ , $b = 75$ , $c = 630$ , and $x = 4$ .

Tap for more steps...

Step 2.4.3.1

Simplify each term.

Tap for more steps...

Step 2.4.3.1.1

Raise $4$ to the power of $2$ .

$y = 20 \cdot 16 + (75) \cdot (4) + 630$

Step 2.4.3.1.2

Multiply $20$ by $16$ .

$y = 320 + (75) \cdot (4) + 630$

Step 2.4.3.1.3

Multiply $75$ by $4$ .

$y = 320 + 300 + 630$

Step 2.4.3.2

Simplify by adding numbers.

Tap for more steps...

Step 2.4.3.2.1

Add $320$ and $300$ .

$y = 620 + 630$

Step 2.4.3.2.2

Add $620$ and $630$ .

$y = 1250$

Step 2.4.4

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 4$ . This check passes since $y = 1250$ and $y = 1250$ .

$1250 = 1250$

Step 2.4.5

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = 20$ , $b = 75$ , $c = 630$ , and $x = 6$ .

Tap for more steps...

Step 2.4.5.1

Simplify each term.

Tap for more steps...

Step 2.4.5.1.1

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

$y = 20 \cdot 36 + (75) \cdot (6) + 630$

Step 2.4.5.1.2

Multiply $20$ by $36$ .

$y = 720 + (75) \cdot (6) + 630$

Step 2.4.5.1.3

Multiply $75$ by $6$ .

$y = 720 + 450 + 630$

Step 2.4.5.2

Simplify by adding numbers.

Tap for more steps...

Step 2.4.5.2.1

Add $720$ and $450$ .

$y = 1170 + 630$

Step 2.4.5.2.2

Add $1170$ and $630$ .

$y = 1800$

Step 2.4.6

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 6$ . This check passes since $y = 1800$ and $y = 1800$ .

$1800 = 1800$

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 $y = 20 x^{2} + 75 x + 630$ .

$y = 20 x^{2} + 75 x + 630$