Solve by Graphing 2x-3y=12 , -x+3/2y=-6

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

Step 1

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

$- 3 y = 12 - 2 x$

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

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 $- 3$ .

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Simplify each term.

Divide $12$ by $- 3$ .

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

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

Dividing two negative values results in a positive value.

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

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

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

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

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

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

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

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

Step 3

Combine $\frac{3}{2}$ and $y$ .

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

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

Step 4

Add $x$ to both sides of the equation.

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

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

Step 5

Multiply both sides of the equation by $\frac{2}{3}$ .

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

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{3} \cdot \frac{3 y}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

Rewrite the expression.

$\frac{1}{3} \cdot (3 y) = \frac{2}{3} \cdot (- 6 + x)$

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

$\frac{1}{3} \cdot (3 y) = \frac{2}{3} \cdot (- 6 + x)$

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 y$ .

$\frac{1}{3} \cdot (3 (y)) = \frac{2}{3} \cdot (- 6 + x)$

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

Cancel the common factor.

$\frac{1}{3} \cdot (3 y) = \frac{2}{3} \cdot (- 6 + x)$

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

Rewrite the expression.

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

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

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

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

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

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

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

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

Simplify the right side.

Simplify $\frac{2}{3} (- 6 + x)$ .

Apply the distributive property.

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

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

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

Cancel the common factor.

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

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

Rewrite the expression.

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

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

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

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

Multiply $2$ by $- 2$ .

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

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

Combine $\frac{2}{3}$ and $x$ .

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

Step 7

Reorder $- 4$ and $\frac{2 x}{3}$ .

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

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

Step 8

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

Always true

Step 9

Solve by Graphing 2x-3y=12 , -x+3/2y=-6

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