Precalculus Examples

$x + 2 y = 8$ , $3 x - 2 y = 0$

Step 1

Subtract $x$ from both sides of the equation.

$2 y = 8 - x$

$3 x - 2 y = 0$

Step 2

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

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Step 2.1

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

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

$3 x - 2 y = 0$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

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

$3 x - 2 y = 0$

Step 2.2.1.2

Divide $y$ by $1$ .

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

$3 x - 2 y = 0$

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

$3 x - 2 y = 0$

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

$3 x - 2 y = 0$

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 $8$ by $2$ .

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

$3 x - 2 y = 0$

Step 2.3.1.2

Move the negative in front of the fraction.

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

$3 x - 2 y = 0$

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

$3 x - 2 y = 0$

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

$3 x - 2 y = 0$

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

$3 x - 2 y = 0$

Step 3

Subtract $3 x$ from both sides of the equation.

$- 2 y = - 3 x$

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

Step 4

Divide each term in $- 2 y = - 3 x$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 y = - 3 x$ by $- 2$ .

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

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

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

Step 4.2.1.2

Divide $y$ by $1$ .

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

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

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

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

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

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

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

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

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

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

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

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

Step 5

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

$(2, 3)$

Step 6