Algebra Examples

$6 a - 2 b - 5 c = 6$ $6 a + 2 b - 2 c = 16$ $a + 4 b + 4 c = 15$

Step 1

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

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Step 1.1

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

$a + 4 c = 15 - 4 b$

$6 a - 2 b - 5 c = 6$

$6 a + 2 b - 2 c = 16$

Step 1.2

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

$a = 15 - 4 b - 4 c$

$6 a - 2 b - 5 c = 6$

$6 a + 2 b - 2 c = 16$

$a = 15 - 4 b - 4 c$

$6 a - 2 b - 5 c = 6$

$6 a + 2 b - 2 c = 16$

Step 2

Replace all occurrences of $a$ with $15 - 4 b - 4 c$ in each equation.

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Step 2.1

Replace all occurrences of $a$ in $6 a - 2 b - 5 c = 6$ with $15 - 4 b - 4 c$ .

$6 (15 - 4 b - 4 c) - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $6 (15 - 4 b - 4 c) - 2 b - 5 c$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$6 \cdot 15 + 6 (- 4 b) + 6 (- 4 c) - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $6$ by $15$ .

$90 + 6 (- 4 b) + 6 (- 4 c) - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.2.1.1.2.2

Multiply $- 4$ by $6$ .

$90 - 24 b + 6 (- 4 c) - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.2.1.1.2.3

Multiply $- 4$ by $6$ .

$90 - 24 b - 24 c - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

$90 - 24 b - 24 c - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

$90 - 24 b - 24 c - 2 b - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $2 b$ from $- 24 b$ .

$90 - 26 b - 24 c - 5 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.2.1.2.2

Subtract $5 c$ from $- 24 c$ .

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$6 a + 2 b - 2 c = 16$

Step 2.3

Replace all occurrences of $a$ in $6 a + 2 b - 2 c = 16$ with $15 - 4 b - 4 c$ .

$6 (15 - 4 b - 4 c) + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $6 (15 - 4 b - 4 c) + 2 b - 2 c$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$6 \cdot 15 + 6 (- 4 b) + 6 (- 4 c) + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $6$ by $15$ .

$90 + 6 (- 4 b) + 6 (- 4 c) + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 2.4.1.1.2.2

Multiply $- 4$ by $6$ .

$90 - 24 b + 6 (- 4 c) + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 2.4.1.1.2.3

Multiply $- 4$ by $6$ .

$90 - 24 b - 24 c + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$90 - 24 b - 24 c + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$90 - 24 b - 24 c + 2 b - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Add $- 24 b$ and $2 b$ .

$90 - 22 b - 24 c - 2 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 2.4.1.2.2

Subtract $2 c$ from $- 24 c$ .

$90 - 22 b - 26 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$90 - 22 b - 26 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$90 - 22 b - 26 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$90 - 22 b - 26 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$90 - 22 b - 26 c = 16$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3

Solve for $b$ in $90 - 22 b - 26 c = 16$ .

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Step 3.1

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

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Step 3.1.1

Subtract $90$ from both sides of the equation.

$- 22 b - 26 c = 16 - 90$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.1.2

Add $26 c$ to both sides of the equation.

$- 22 b = 16 - 90 + 26 c$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.1.3

Subtract $90$ from $16$ .

$- 22 b = - 74 + 26 c$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$- 22 b = - 74 + 26 c$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2

Divide each term in $- 22 b = - 74 + 26 c$ by $- 22$ and simplify.

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Step 3.2.1

Divide each term in $- 22 b = - 74 + 26 c$ by $- 22$ .

$\frac{- 22 b}{- 22} = \frac{- 74}{- 22} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 22$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 22 b}{- 22} = \frac{- 74}{- 22} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.2.1.2

Divide $b$ by $1$ .

$b = \frac{- 74}{- 22} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{- 74}{- 22} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{- 74}{- 22} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Cancel the common factor of $- 74$ and $- 22$ .

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Step 3.2.3.1.1.1

Factor $- 2$ out of $- 74$ .

$b = \frac{- 2 \cdot 37}{- 22} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.1.2

Cancel the common factors.

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Step 3.2.3.1.1.2.1

Factor $- 2$ out of $- 22$ .

$b = \frac{- 2 \cdot 37}{- 2 \cdot 11} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.1.2.2

Cancel the common factor.

$b = \frac{- 2 \cdot 37}{- 2 \cdot 11} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.1.2.3

Rewrite the expression.

$b = \frac{37}{11} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} + \frac{26 c}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.2

Cancel the common factor of $26$ and $- 22$ .

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Step 3.2.3.1.2.1

Factor $2$ out of $26 c$ .

$b = \frac{37}{11} + \frac{2 (13 c)}{- 22}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.2.2

Cancel the common factors.

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Step 3.2.3.1.2.2.1

Factor $2$ out of $- 22$ .

$b = \frac{37}{11} + \frac{2 (13 c)}{2 (- 11)}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.2.2.2

Cancel the common factor.

$b = \frac{37}{11} + \frac{2 (13 c)}{2 \cdot - 11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.2.2.3

Rewrite the expression.

$b = \frac{37}{11} + \frac{13 c}{- 11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} + \frac{13 c}{- 11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} + \frac{13 c}{- 11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 3.2.3.1.3

Move the negative in front of the fraction.

$b = \frac{37}{11} - \frac{13 c}{11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} - \frac{13 c}{11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} - \frac{13 c}{11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} - \frac{13 c}{11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

$b = \frac{37}{11} - \frac{13 c}{11}$

$90 - 26 b - 29 c = 6$

$a = 15 - 4 b - 4 c$

Step 4

Replace all occurrences of $b$ with $\frac{37}{11} - \frac{13 c}{11}$ in each equation.

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Step 4.1

Replace all occurrences of $b$ in $90 - 26 b - 29 c = 6$ with $\frac{37}{11} - \frac{13 c}{11}$ .

$90 - 26 (\frac{37}{11} - \frac{13 c}{11}) - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $90 - 26 (\frac{37}{11} - \frac{13 c}{11}) - 29 c$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Apply the distributive property.

$90 - 26 (\frac{37}{11}) - 26 (- \frac{13 c}{11}) - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.1.2

Multiply $- 26 (\frac{37}{11})$ .

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Step 4.2.1.1.2.1

Combine $- 26$ and $\frac{37}{11}$ .

$90 + \frac{- 26 \cdot 37}{11} - 26 (- \frac{13 c}{11}) - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.1.2.2

Multiply $- 26$ by $37$ .

$90 + \frac{- 962}{11} - 26 (- \frac{13 c}{11}) - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

$90 + \frac{- 962}{11} - 26 (- \frac{13 c}{11}) - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.1.3

Multiply $- 26 (- \frac{13 c}{11})$ .

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Step 4.2.1.1.3.1

Multiply $- 1$ by $- 26$ .

$90 + \frac{- 962}{11} + 26 (\frac{13 c}{11}) - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.1.3.2

Combine $26$ and $\frac{13 c}{11}$ .

$90 + \frac{- 962}{11} + \frac{26 (13 c)}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.1.3.3

Multiply $13$ by $26$ .

$90 + \frac{- 962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

$90 + \frac{- 962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.1.4

Move the negative in front of the fraction.

$90 - \frac{962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

$90 - \frac{962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.2

To write $90$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$90 \cdot \frac{11}{11} - \frac{962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.3

Combine $90$ and $\frac{11}{11}$ .

$\frac{90 \cdot 11}{11} - \frac{962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.4

Combine the numerators over the common denominator.

$\frac{90 \cdot 11 - 962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $90$ by $11$ .

$\frac{990 - 962}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.5.2

Subtract $962$ from $990$ .

$\frac{28}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

$\frac{28}{11} + \frac{338 c}{11} - 29 c = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.6

To write $- 29 c$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{28}{11} + \frac{338 c}{11} - 29 c \cdot \frac{11}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.7

Combine $- 29 c$ and $\frac{11}{11}$ .

$\frac{28}{11} + \frac{338 c}{11} + \frac{- 29 c \cdot 11}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.8

Combine the numerators over the common denominator.

$\frac{28}{11} + \frac{338 c - 29 c \cdot 11}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.9

Combine the numerators over the common denominator.

$\frac{28 + 338 c - 29 c \cdot 11}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.10

Multiply $11$ by $- 29$ .

$\frac{28 + 338 c - 319 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.2.1.11

Subtract $319 c$ from $338 c$ .

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - 4 b - 4 c$

Step 4.3

Replace all occurrences of $b$ in $a = 15 - 4 b - 4 c$ with $\frac{37}{11} - \frac{13 c}{11}$ .

$a = 15 - 4 (\frac{37}{11} - \frac{13 c}{11}) - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $15 - 4 (\frac{37}{11} - \frac{13 c}{11}) - 4 c$ .

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Step 4.4.1.1

Simplify each term.

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Step 4.4.1.1.1

Apply the distributive property.

$a = 15 - 4 (\frac{37}{11}) - 4 (- \frac{13 c}{11}) - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.1.2

Multiply $- 4 (\frac{37}{11})$ .

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Step 4.4.1.1.2.1

Combine $- 4$ and $\frac{37}{11}$ .

$a = 15 + \frac{- 4 \cdot 37}{11} - 4 (- \frac{13 c}{11}) - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.1.2.2

Multiply $- 4$ by $37$ .

$a = 15 + \frac{- 148}{11} - 4 (- \frac{13 c}{11}) - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 + \frac{- 148}{11} - 4 (- \frac{13 c}{11}) - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.1.3

Multiply $- 4 (- \frac{13 c}{11})$ .

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 4$ .

$a = 15 + \frac{- 148}{11} + 4 (\frac{13 c}{11}) - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.1.3.2

Combine $4$ and $\frac{13 c}{11}$ .

$a = 15 + \frac{- 148}{11} + \frac{4 (13 c)}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.1.3.3

Multiply $13$ by $4$ .

$a = 15 + \frac{- 148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 + \frac{- 148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$a = 15 - \frac{148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 15 - \frac{148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.2

To write $15$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$a = 15 \cdot \frac{11}{11} - \frac{148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.3

Combine $15$ and $\frac{11}{11}$ .

$a = \frac{15 \cdot 11}{11} - \frac{148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$a = \frac{15 \cdot 11 - 148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $15$ by $11$ .

$a = \frac{165 - 148}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.5.2

Subtract $148$ from $165$ .

$a = \frac{17}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = \frac{17}{11} + \frac{52 c}{11} - 4 c$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.6

To write $- 4 c$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$a = \frac{17}{11} + \frac{52 c}{11} - 4 c \cdot \frac{11}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.7

Combine $- 4 c$ and $\frac{11}{11}$ .

$a = \frac{17}{11} + \frac{52 c}{11} + \frac{- 4 c \cdot 11}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.8

Combine the numerators over the common denominator.

$a = \frac{17}{11} + \frac{52 c - 4 c \cdot 11}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$a = \frac{17 + 52 c - 4 c \cdot 11}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.10

Multiply $11$ by $- 4$ .

$a = \frac{17 + 52 c - 44 c}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 4.4.1.11

Subtract $44 c$ from $52 c$ .

$a = \frac{17 + 8 c}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = \frac{17 + 8 c}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = \frac{17 + 8 c}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = \frac{17 + 8 c}{11}$

$\frac{28 + 19 c}{11} = 6$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5

Solve for $c$ in $\frac{28 + 19 c}{11} = 6$ .

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Step 5.1

Multiply both sides by $11$ .

$\frac{28 + 19 c}{11} \cdot 11 = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.2

Simplify.

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Step 5.2.1

Simplify the left side.

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Step 5.2.1.1

Simplify $\frac{28 + 19 c}{11} \cdot 11$ .

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Step 5.2.1.1.1

Cancel the common factor of $11$ .

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Step 5.2.1.1.1.1

Cancel the common factor.

$\frac{28 + 19 c}{11} \cdot 11 = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.2.1.1.1.2

Rewrite the expression.

$28 + 19 c = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$28 + 19 c = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.2.1.1.2

Reorder $28$ and $19 c$ .

$19 c + 28 = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$19 c + 28 = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$19 c + 28 = 6 \cdot 11$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.2.2

Simplify the right side.

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Step 5.2.2.1

Multiply $6$ by $11$ .

$19 c + 28 = 66$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$19 c + 28 = 66$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$19 c + 28 = 66$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.3

Solve for $c$ .

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Step 5.3.1

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

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Step 5.3.1.1

Subtract $28$ from both sides of the equation.

$19 c = 66 - 28$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.3.1.2

Subtract $28$ from $66$ .

$19 c = 38$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$19 c = 38$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.3.2

Divide each term in $19 c = 38$ by $19$ and simplify.

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Step 5.3.2.1

Divide each term in $19 c = 38$ by $19$ .

$\frac{19 c}{19} = \frac{38}{19}$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.3.2.2

Simplify the left side.

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Step 5.3.2.2.1

Cancel the common factor of $19$ .

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Step 5.3.2.2.1.1

Cancel the common factor.

$\frac{19 c}{19} = \frac{38}{19}$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.3.2.2.1.2

Divide $c$ by $1$ .

$c = \frac{38}{19}$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$c = \frac{38}{19}$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$c = \frac{38}{19}$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 5.3.2.3

Simplify the right side.

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Step 5.3.2.3.1

Divide $38$ by $19$ .

$c = 2$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$c = 2$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$c = 2$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$c = 2$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

$c = 2$

$a = \frac{17 + 8 c}{11}$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 6

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

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Step 6.1

Replace all occurrences of $c$ in $a = \frac{17 + 8 c}{11}$ with $2$ .

$a = \frac{17 + 8 (2)}{11}$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{17 + 8 (2)}{11}$ .

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Step 6.2.1.1

Simplify the numerator.

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Step 6.2.1.1.1

Multiply $8$ by $2$ .

$a = \frac{17 + 16}{11}$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 6.2.1.1.2

Add $17$ and $16$ .

$a = \frac{33}{11}$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = \frac{33}{11}$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 6.2.1.2

Divide $33$ by $11$ .

$a = 3$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 3$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

$a = 3$

$c = 2$

$b = \frac{37}{11} - \frac{13 c}{11}$

Step 6.3

Replace all occurrences of $c$ in $b = \frac{37}{11} - \frac{13 c}{11}$ with $2$ .

$b = \frac{37}{11} - \frac{13 (2)}{11}$

$a = 3$

$c = 2$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{37}{11} - \frac{13 (2)}{11}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$b = \frac{37 - 13 \cdot 2}{11}$

$a = 3$

$c = 2$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $- 13$ by $2$ .

$b = \frac{37 - 26}{11}$

$a = 3$

$c = 2$

Step 6.4.1.2.2

Subtract $26$ from $37$ .

$b = \frac{11}{11}$

$a = 3$

$c = 2$

Step 6.4.1.2.3

Divide $11$ by $11$ .

$b = 1$

$a = 3$

$c = 2$

$b = 1$

$a = 3$

$c = 2$

$b = 1$

$a = 3$

$c = 2$

$b = 1$

$a = 3$

$c = 2$

$b = 1$

$a = 3$

$c = 2$

Step 7

List all of the solutions.

$b = 1, a = 3, c = 2$