Solve by Graphing 2x+3y=12 2x-y=4

$2 x + 3 y = 12$ $2 x - y = 4$

Step 1

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

$3 y = 12 - 2 x$

$2 x - y = 4$

Step 2

Divide each term in $3 y = 12 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = 12 - 2 x$ by $3$ .

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

$2 x - y = 4$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$2 x - y = 4$

Divide $y$ by $1$ .

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

$2 x - y = 4$

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

$2 x - y = 4$

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

$2 x - y = 4$

Simplify the right side.

Simplify each term.

Divide $12$ by $3$ .

$y = 4 + \frac{- 2 x}{3}$

$2 x - y = 4$

Move the negative in front of the fraction.

$y = 4 - \frac{2 x}{3}$

$2 x - y = 4$

$y = 4 - \frac{2 x}{3}$

$2 x - y = 4$

$y = 4 - \frac{2 x}{3}$

$2 x - y = 4$

$y = 4 - \frac{2 x}{3}$

$2 x - y = 4$

Step 3

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

$- y = 4 - 2 x$

$y = 4 - \frac{2 x}{3}$

Step 4

Divide each term in $- y = 4 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = 4 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{4}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 - \frac{2 x}{3}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{4}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 - \frac{2 x}{3}$

Divide $y$ by $1$ .

$y = \frac{4}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 - \frac{2 x}{3}$

$y = \frac{4}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 - \frac{2 x}{3}$

Simplify the right side.

Simplify each term.

Divide $4$ by $- 1$ .

$y = - 4 + \frac{- 2 x}{- 1}$

$y = 4 - \frac{2 x}{3}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y = - 4 - 1 \cdot (- 2 x)$

$y = 4 - \frac{2 x}{3}$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = - 4 - (- 2 x)$

$y = 4 - \frac{2 x}{3}$

Multiply $- 2$ by $- 1$ .

$y = - 4 + 2 x$

$y = 4 - \frac{2 x}{3}$

$y = - 4 + 2 x$

$y = 4 - \frac{2 x}{3}$

$y = - 4 + 2 x$

$y = 4 - \frac{2 x}{3}$

$y = - 4 + 2 x$

$y = 4 - \frac{2 x}{3}$

Step 5

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

$(3, 2)$

Step 6

Solve by Graphing 2x+3y=12 2x-y=4

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