Algebra Examples

$9 y = - 17 x + 72$ $- 72 + 17 x = - 9 y$

Step 1

Divide each term in $9 y = - 17 x + 72$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 y = - 17 x + 72$ by $9$ .

$\frac{9 y}{9} = \frac{- 17 x}{9} + \frac{72}{9}$

$- 72 + 17 x = - 9 y$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $9$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 17 x}{9} + \frac{72}{9}$

$- 72 + 17 x = - 9 y$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 17 x}{9} + \frac{72}{9}$

$- 72 + 17 x = - 9 y$

$y = \frac{- 17 x}{9} + \frac{72}{9}$

$- 72 + 17 x = - 9 y$

$y = \frac{- 17 x}{9} + \frac{72}{9}$

$- 72 + 17 x = - 9 y$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Move the negative in front of the fraction.

$y = - \frac{17 x}{9} + \frac{72}{9}$

$- 72 + 17 x = - 9 y$

Step 1.3.1.2

Divide $72$ by $9$ .

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = - 9 y$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = - 9 y$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = - 9 y$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = - 9 y$

Step 2

Replace all occurrences of $y$ with $- \frac{17 x}{9} + 8$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 72 + 17 x = - 9 y$ with $- \frac{17 x}{9} + 8$ .

$- 72 + 17 x = - 9 (- \frac{17 x}{9} + 8)$

$y = - \frac{17 x}{9} + 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- 9 (- \frac{17 x}{9} + 8)$ .

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Step 2.2.1.1

Apply the distributive property.

$- 72 + 17 x = - 9 (- \frac{17 x}{9}) - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

Step 2.2.1.2

Cancel the common factor of $9$ .

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Step 2.2.1.2.1

Move the leading negative in $- \frac{17 x}{9}$ into the numerator.

$- 72 + 17 x = - 9 \frac{- 17 x}{9} - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

Step 2.2.1.2.2

Factor $9$ out of $- 9$ .

$- 72 + 17 x = 9 (- 1) (\frac{- 17 x}{9}) - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

Step 2.2.1.2.3

Cancel the common factor.

$- 72 + 17 x = 9 \cdot (- 1 \frac{- 17 x}{9}) - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

Step 2.2.1.2.4

Rewrite the expression.

$- 72 + 17 x = - 1 (- 17 x) - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = - 1 (- 17 x) - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

Step 2.2.1.3

Multiply.

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Step 2.2.1.3.1

Multiply $- 17$ by $- 1$ .

$- 72 + 17 x = 17 x - 9 \cdot 8$

$y = - \frac{17 x}{9} + 8$

Step 2.2.1.3.2

Multiply $- 9$ by $8$ .

$- 72 + 17 x = 17 x - 72$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = 17 x - 72$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = 17 x - 72$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = 17 x - 72$

$y = - \frac{17 x}{9} + 8$

$- 72 + 17 x = 17 x - 72$

$y = - \frac{17 x}{9} + 8$

Step 3

Solve for $x$ in $- 72 + 17 x = 17 x - 72$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $17 x$ from both sides of the equation.

$- 72 + 17 x - 17 x = - 72$

$y = - \frac{17 x}{9} + 8$

Step 3.1.2

Combine the opposite terms in $- 72 + 17 x - 17 x$ .

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Step 3.1.2.1

Subtract $17 x$ from $17 x$ .

$- 72 + 0 = - 72$

$y = - \frac{17 x}{9} + 8$

Step 3.1.2.2

Add $- 72$ and $0$ .

$- 72 = - 72$

$y = - \frac{17 x}{9} + 8$

$- 72 = - 72$

$y = - \frac{17 x}{9} + 8$

$- 72 = - 72$

$y = - \frac{17 x}{9} + 8$

Step 3.2

Since $- 72 = - 72$ , the equation will always be true.

Always true

$y = - \frac{17 x}{9} + 8$

Always true

$y = - \frac{17 x}{9} + 8$

Step 4

Remove any equations from the system that are always true.

$y = - \frac{17 x}{9} + 8$

Step 5