Solve by Graphing -7x-2y=14 , 6x+6y=18

$- 7 x - 2 y = 14$ , $6 x + 6 y = 18$

Step 1

Add $7 x$ to both sides of the equation.

$- 2 y = 14 + 7 x$

$6 x + 6 y = 18$

Step 2

Divide each term in $- 2 y = 14 + 7 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 14 + 7 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{14}{- 2} + \frac{7 x}{- 2}$

$6 x + 6 y = 18$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{14}{- 2} + \frac{7 x}{- 2}$

$6 x + 6 y = 18$

Divide $y$ by $1$ .

$y = \frac{14}{- 2} + \frac{7 x}{- 2}$

$6 x + 6 y = 18$

$y = \frac{14}{- 2} + \frac{7 x}{- 2}$

$6 x + 6 y = 18$

$y = \frac{14}{- 2} + \frac{7 x}{- 2}$

$6 x + 6 y = 18$

Simplify the right side.

Simplify each term.

Divide $14$ by $- 2$ .

$y = - 7 + \frac{7 x}{- 2}$

$6 x + 6 y = 18$

Move the negative in front of the fraction.

$y = - 7 - \frac{7 x}{2}$

$6 x + 6 y = 18$

$y = - 7 - \frac{7 x}{2}$

$6 x + 6 y = 18$

$y = - 7 - \frac{7 x}{2}$

$6 x + 6 y = 18$

$y = - 7 - \frac{7 x}{2}$

$6 x + 6 y = 18$

Step 3

Subtract $6 x$ from both sides of the equation.

$6 y = 18 - 6 x$

$y = - 7 - \frac{7 x}{2}$

Step 4

Divide each term in $6 y = 18 - 6 x$ by $6$ and simplify.

Divide each term in $6 y = 18 - 6 x$ by $6$ .

$\frac{6 y}{6} = \frac{18}{6} + \frac{- 6 x}{6}$

$y = - 7 - \frac{7 x}{2}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{18}{6} + \frac{- 6 x}{6}$

$y = - 7 - \frac{7 x}{2}$

Divide $y$ by $1$ .

$y = \frac{18}{6} + \frac{- 6 x}{6}$

$y = - 7 - \frac{7 x}{2}$

$y = \frac{18}{6} + \frac{- 6 x}{6}$

$y = - 7 - \frac{7 x}{2}$

$y = \frac{18}{6} + \frac{- 6 x}{6}$

$y = - 7 - \frac{7 x}{2}$

Simplify the right side.

Simplify each term.

Divide $18$ by $6$ .

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

$y = - 7 - \frac{7 x}{2}$

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

Factor $6$ out of $- 6 x$ .

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

$y = - 7 - \frac{7 x}{2}$

Cancel the common factors.

Factor $6$ out of $6$ .

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

$y = - 7 - \frac{7 x}{2}$

Cancel the common factor.

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

$y = - 7 - \frac{7 x}{2}$

Rewrite the expression.

$y = 3 + \frac{- x}{1}$

$y = - 7 - \frac{7 x}{2}$

Divide $- x$ by $1$ .

$y = 3 - x$

$y = - 7 - \frac{7 x}{2}$

$y = 3 - x$

$y = - 7 - \frac{7 x}{2}$

$y = 3 - x$

$y = - 7 - \frac{7 x}{2}$

$y = 3 - x$

$y = - 7 - \frac{7 x}{2}$

$y = 3 - x$

$y = - 7 - \frac{7 x}{2}$

$y = 3 - x$

$y = - 7 - \frac{7 x}{2}$

Step 5

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

$(- 4, 7)$

Step 6

Solve by Graphing -7x-2y=14 , 6x+6y=18

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