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

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

Step 1

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

$6 y = 12 - 4 x$

$2 x + 3 y = - 6$

Step 2

Divide each term in $6 y = 12 - 4 x$ by $6$ and simplify.

Divide each term in $6 y = 12 - 4 x$ by $6$ .

$\frac{6 y}{6} = \frac{12}{6} + \frac{- 4 x}{6}$

$2 x + 3 y = - 6$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{12}{6} + \frac{- 4 x}{6}$

$2 x + 3 y = - 6$

Divide $y$ by $1$ .

$y = \frac{12}{6} + \frac{- 4 x}{6}$

$2 x + 3 y = - 6$

$y = \frac{12}{6} + \frac{- 4 x}{6}$

$2 x + 3 y = - 6$

$y = \frac{12}{6} + \frac{- 4 x}{6}$

$2 x + 3 y = - 6$

Simplify the right side.

Simplify each term.

Divide $12$ by $6$ .

$y = 2 + \frac{- 4 x}{6}$

$2 x + 3 y = - 6$

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $- 4 x$ .

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

$2 x + 3 y = - 6$

Cancel the common factors.

Factor $2$ out of $6$ .

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

$2 x + 3 y = - 6$

Cancel the common factor.

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

$2 x + 3 y = - 6$

Rewrite the expression.

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

$2 x + 3 y = - 6$

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

$2 x + 3 y = - 6$

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

$2 x + 3 y = - 6$

Move the negative in front of the fraction.

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

$2 x + 3 y = - 6$

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

$2 x + 3 y = - 6$

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

$2 x + 3 y = - 6$

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

$2 x + 3 y = - 6$

Step 3

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

$3 y = - 6 - 2 x$

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

Step 4

Divide each term in $3 y = - 6 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = - 6 - 2 x$ by $3$ .

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Simplify each term.

Divide $- 6$ by $3$ .

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 5

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

No solution

Step 6

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

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