Solve by Graphing 2x+y=-7 , -6y=12x+42

$2 x + y = - 7$ , $- 6 y = 12 x + 42$

Step 1

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

$y = - 7 - 2 x$

$- 6 y = 12 x + 42$

Step 2

Divide each term in $- 6 y = 12 x + 42$ by $- 6$ and simplify.

Divide each term in $- 6 y = 12 x + 42$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{12 x}{- 6} + \frac{42}{- 6}$

$y = - 7 - 2 x$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{12 x}{- 6} + \frac{42}{- 6}$

$y = - 7 - 2 x$

Divide $y$ by $1$ .

$y = \frac{12 x}{- 6} + \frac{42}{- 6}$

$y = - 7 - 2 x$

$y = \frac{12 x}{- 6} + \frac{42}{- 6}$

$y = - 7 - 2 x$

$y = \frac{12 x}{- 6} + \frac{42}{- 6}$

$y = - 7 - 2 x$

Simplify the right side.

Simplify each term.

Cancel the common factor of $12$ and $- 6$ .

Factor $6$ out of $12 x$ .

$y = \frac{6 (2 x)}{- 6} + \frac{42}{- 6}$

$y = - 7 - 2 x$

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

$y = - 1 \cdot (2 x) + \frac{42}{- 6}$

$y = - 7 - 2 x$

$y = - 1 \cdot (2 x) + \frac{42}{- 6}$

$y = - 7 - 2 x$

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

$y = - (2 x) + \frac{42}{- 6}$

$y = - 7 - 2 x$

Multiply $2$ by $- 1$ .

$y = - 2 x + \frac{42}{- 6}$

$y = - 7 - 2 x$

Divide $42$ by $- 6$ .

$y = - 2 x - 7$

$y = - 7 - 2 x$

$y = - 2 x - 7$

$y = - 7 - 2 x$

$y = - 2 x - 7$

$y = - 7 - 2 x$

$y = - 2 x - 7$

$y = - 7 - 2 x$

Step 3

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

Always true

Step 4

Solve by Graphing 2x+y=-7 , -6y=12x+42

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