Precalculus Examples

$5 x - 6 y = 12$ , $2 x - 4 y = 8$

Step 1

Subtract $5 x$ from both sides of the equation.

$- 6 y = 12 - 5 x$

$2 x - 4 y = 8$

Step 2

Divide each term in $- 6 y = 12 - 5 x$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 y = 12 - 5 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

$2 x - 4 y = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

$2 x - 4 y = 8$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

$2 x - 4 y = 8$

$y = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

$2 x - 4 y = 8$

$y = \frac{12}{- 6} + \frac{- 5 x}{- 6}$

$2 x - 4 y = 8$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $12$ by $- 6$ .

$y = - 2 + \frac{- 5 x}{- 6}$

$2 x - 4 y = 8$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = - 2 + \frac{5 x}{6}$

$2 x - 4 y = 8$

$y = - 2 + \frac{5 x}{6}$

$2 x - 4 y = 8$

$y = - 2 + \frac{5 x}{6}$

$2 x - 4 y = 8$

$y = - 2 + \frac{5 x}{6}$

$2 x - 4 y = 8$

Step 3

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

$- 4 y = 8 - 2 x$

$y = - 2 + \frac{5 x}{6}$

Step 4

Divide each term in $- 4 y = 8 - 2 x$ by $- 4$ and simplify.

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Step 4.1

Divide each term in $- 4 y = 8 - 2 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

$y = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

$y = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

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

Divide $8$ by $- 4$ .

$y = - 2 + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

Step 4.3.1.2

Cancel the common factor of $- 2$ and $- 4$ .

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Step 4.3.1.2.1

Factor $- 2$ out of $- 2 x$ .

$y = - 2 + \frac{- 2 x}{- 4}$

$y = - 2 + \frac{5 x}{6}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $- 2$ out of $- 4$ .

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

$y = - 2 + \frac{5 x}{6}$

Step 4.3.1.2.2.2

Cancel the common factor.

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

$y = - 2 + \frac{5 x}{6}$

Step 4.3.1.2.2.3

Rewrite the expression.

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

$y = - 2 + \frac{5 x}{6}$

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

$y = - 2 + \frac{5 x}{6}$

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

$y = - 2 + \frac{5 x}{6}$

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

$y = - 2 + \frac{5 x}{6}$

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

$y = - 2 + \frac{5 x}{6}$

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

$y = - 2 + \frac{5 x}{6}$

Step 5

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

$(0, - 2)$

Step 6