Solve by Graphing 4x-3y=-2 , -12x+9y=6

$4 x - 3 y = - 2$ , $- 12 x + 9 y = 6$

Step 1

Subtract $4 x$ from both sides of the equation.

$- 3 y = - 2 - 4 x$

$- 12 x + 9 y = 6$

Step 2

Divide each term in $- 3 y = - 2 - 4 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 2 - 4 x$ by $- 3$ .

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

$- 12 x + 9 y = 6$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$- 12 x + 9 y = 6$

Divide $y$ by $1$ .

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

$- 12 x + 9 y = 6$

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

$- 12 x + 9 y = 6$

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

$- 12 x + 9 y = 6$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

$- 12 x + 9 y = 6$

Dividing two negative values results in a positive value.

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

$- 12 x + 9 y = 6$

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

$- 12 x + 9 y = 6$

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

$- 12 x + 9 y = 6$

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

$- 12 x + 9 y = 6$

Step 3

Add $12 x$ to both sides of the equation.

$9 y = 6 + 12 x$

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

Step 4

Divide each term in $9 y = 6 + 12 x$ by $9$ and simplify.

Divide each term in $9 y = 6 + 12 x$ by $9$ .

$\frac{9 y}{9} = \frac{6}{9} + \frac{12 x}{9}$

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

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{6}{9} + \frac{12 x}{9}$

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

Divide $y$ by $1$ .

$y = \frac{6}{9} + \frac{12 x}{9}$

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

$y = \frac{6}{9} + \frac{12 x}{9}$

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

$y = \frac{6}{9} + \frac{12 x}{9}$

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $9$ .

Factor $3$ out of $6$ .

$y = \frac{3 (2)}{9} + \frac{12 x}{9}$

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

Cancel the common factors.

Factor $3$ out of $9$ .

$y = \frac{3 \cdot 2}{3 \cdot 3} + \frac{12 x}{9}$

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

Cancel the common factor.

$y = \frac{3 \cdot 2}{3 \cdot 3} + \frac{12 x}{9}$

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

Rewrite the expression.

$y = \frac{2}{3} + \frac{12 x}{9}$

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

$y = \frac{2}{3} + \frac{12 x}{9}$

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

$y = \frac{2}{3} + \frac{12 x}{9}$

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

Cancel the common factor of $12$ and $9$ .

Factor $3$ out of $12 x$ .

$y = \frac{2}{3} + \frac{3 (4 x)}{9}$

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

Cancel the common factors.

Factor $3$ out of $9$ .

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

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

Cancel the common factor.

$y = \frac{2}{3} + \frac{3 (4 x)}{3 \cdot 3}$

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

Step 5

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

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

Step 6

Related Questions