Precalculus Examples

$- 2 = x - 2 y$ , $16 = 2 x + y$ , $- 4 = x + 2 y$

Step 1

Rewrite the equation as $x - 2 y = - 2$ .

$x - 2 y = - 2$

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 2

Subtract $x$ from both sides of the equation.

$- 2 y = - 2 - x$

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 3

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

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Step 3.1

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

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

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

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

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 3.2.1.2

Divide $y$ by $1$ .

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

$16 = 2 x + y$

$- 4 = x + 2 y$

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

$16 = 2 x + y$

$- 4 = x + 2 y$

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

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $- 2$ by $- 2$ .

$y = 1 + \frac{- x}{- 2}$

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$y = 1 + \frac{x}{2}$

$16 = 2 x + y$

$- 4 = x + 2 y$

$y = 1 + \frac{x}{2}$

$16 = 2 x + y$

$- 4 = x + 2 y$

$y = 1 + \frac{x}{2}$

$16 = 2 x + y$

$- 4 = x + 2 y$

$y = 1 + \frac{x}{2}$

$16 = 2 x + y$

$- 4 = x + 2 y$

Step 4

Rewrite the equation as $2 x + y = 16$ .

$2 x + y = 16$

$y = 1 + \frac{x}{2}$

$- 4 = x + 2 y$

Step 5

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

$y = 16 - 2 x$

$y = 1 + \frac{x}{2}$

$- 4 = x + 2 y$

Step 6

Rewrite the equation as $x + 2 y = - 4$ .

$x + 2 y = - 4$

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 7

Subtract $x$ from both sides of the equation.

$2 y = - 4 - x$

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 8

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

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Step 8.1

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

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $2$ .

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Step 8.2.1.1

Cancel the common factor.

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 8.2.1.2

Divide $y$ by $1$ .

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 8.3

Simplify the right side.

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

Divide $- 4$ by $2$ .

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 8.3.1.2

Move the negative in front of the fraction.

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

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

$y = 1 + \frac{x}{2}$

$y = 16 - 2 x$

Step 9

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

$(6, - 5)$

Step 10