Precalculus Examples

$8 x + 8 y = 0$ , $- 12 x - 12 y = 18$

Step 1

Subtract $8 x$ from both sides of the equation.

$8 y = - 8 x$

$- 12 x - 12 y = 18$

Step 2

Divide each term in $8 y = - 8 x$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 y = - 8 x$ by $8$ .

$\frac{8 y}{8} = \frac{- 8 x}{8}$

$- 12 x - 12 y = 18$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 8 x}{8}$

$- 12 x - 12 y = 18$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 8 x}{8}$

$- 12 x - 12 y = 18$

$y = \frac{- 8 x}{8}$

$- 12 x - 12 y = 18$

$y = \frac{- 8 x}{8}$

$- 12 x - 12 y = 18$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $- 8$ and $8$ .

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Step 2.3.1.1

Factor $8$ out of $- 8 x$ .

$y = \frac{8 (- x)}{8}$

$- 12 x - 12 y = 18$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $8$ out of $8$ .

$y = \frac{8 (- x)}{8 (1)}$

$- 12 x - 12 y = 18$

Step 2.3.1.2.2

Cancel the common factor.

$y = \frac{8 (- x)}{8 \cdot 1}$

$- 12 x - 12 y = 18$

Step 2.3.1.2.3

Rewrite the expression.

$y = \frac{- x}{1}$

$- 12 x - 12 y = 18$

Step 2.3.1.2.4

Divide $- x$ by $1$ .

$y = - x$

$- 12 x - 12 y = 18$

$y = - x$

$- 12 x - 12 y = 18$

$y = - x$

$- 12 x - 12 y = 18$

$y = - x$

$- 12 x - 12 y = 18$

$y = - x$

$- 12 x - 12 y = 18$

Step 3

Add $12 x$ to both sides of the equation.

$- 12 y = 18 + 12 x$

$y = - x$

Step 4

Divide each term in $- 12 y = 18 + 12 x$ by $- 12$ and simplify.

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Step 4.1

Divide each term in $- 12 y = 18 + 12 x$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{18}{- 12} + \frac{12 x}{- 12}$

$y = - x$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 12$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{18}{- 12} + \frac{12 x}{- 12}$

$y = - x$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{- 12} + \frac{12 x}{- 12}$

$y = - x$

$y = \frac{18}{- 12} + \frac{12 x}{- 12}$

$y = - x$

$y = \frac{18}{- 12} + \frac{12 x}{- 12}$

$y = - x$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $18$ and $- 12$ .

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Step 4.3.1.1.1

Factor $6$ out of $18$ .

$y = \frac{6 (3)}{- 12} + \frac{12 x}{- 12}$

$y = - x$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Factor $6$ out of $- 12$ .

$y = \frac{6 \cdot 3}{6 \cdot - 2} + \frac{12 x}{- 12}$

$y = - x$

Step 4.3.1.1.2.2

Cancel the common factor.

$y = \frac{6 \cdot 3}{6 \cdot - 2} + \frac{12 x}{- 12}$

$y = - x$

Step 4.3.1.1.2.3

Rewrite the expression.

$y = \frac{3}{- 2} + \frac{12 x}{- 12}$

$y = - x$

$y = \frac{3}{- 2} + \frac{12 x}{- 12}$

$y = - x$

$y = \frac{3}{- 2} + \frac{12 x}{- 12}$

$y = - x$

Step 4.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3}{2} + \frac{12 x}{- 12}$

$y = - x$

Step 4.3.1.3

Cancel the common factor of $12$ and $- 12$ .

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Step 4.3.1.3.1

Factor $12$ out of $12 x$ .

$y = - \frac{3}{2} + \frac{12 (x)}{- 12}$

$y = - x$

Step 4.3.1.3.2

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y = - \frac{3}{2} - 1 \cdot x$

$y = - x$

$y = - \frac{3}{2} - 1 \cdot x$

$y = - x$

Step 4.3.1.4

Rewrite $- 1 \cdot x$ as $- x$ .

$y = - \frac{3}{2} - x$

$y = - x$

$y = - \frac{3}{2} - x$

$y = - x$

$y = - \frac{3}{2} - x$

$y = - x$

$y = - \frac{3}{2} - x$

$y = - x$

Step 5

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

No solution

Step 6