Solve by Graphing 2x=-1-y , 2y=6x+5

$2 x = - 1 - y$ , $2 y = 6 x + 5$

Step 1

Rewrite the equation as $- 1 - y = 2 x$ .

$- 1 - y = 2 x$

$2 y = 6 x + 5$

Step 2

Add $1$ to both sides of the equation.

$- y = 2 x + 1$

$2 y = 6 x + 5$

Step 3

Divide each term in $- y = 2 x + 1$ by $- 1$ and simplify.

Divide each term in $- y = 2 x + 1$ by $- 1$ .

$\frac{- y}{- 1} = \frac{2 x}{- 1} + \frac{1}{- 1}$

$2 y = 6 x + 5$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{2 x}{- 1} + \frac{1}{- 1}$

$2 y = 6 x + 5$

Divide $y$ by $1$ .

$y = \frac{2 x}{- 1} + \frac{1}{- 1}$

$2 y = 6 x + 5$

$y = \frac{2 x}{- 1} + \frac{1}{- 1}$

$2 y = 6 x + 5$

Simplify the right side.

Simplify each term.

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

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

$2 y = 6 x + 5$

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

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

$2 y = 6 x + 5$

Multiply $2$ by $- 1$ .

$y = - 2 x + \frac{1}{- 1}$

$2 y = 6 x + 5$

Divide $1$ by $- 1$ .

$y = - 2 x - 1$

$2 y = 6 x + 5$

$y = - 2 x - 1$

$2 y = 6 x + 5$

$y = - 2 x - 1$

$2 y = 6 x + 5$

$y = - 2 x - 1$

$2 y = 6 x + 5$

Step 4

Divide each term in $2 y = 6 x + 5$ by $2$ and simplify.

Divide each term in $2 y = 6 x + 5$ by $2$ .

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{5}{2}$

$y = - 2 x - 1$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{5}{2}$

$y = - 2 x - 1$

Divide $y$ by $1$ .

$y = \frac{6 x}{2} + \frac{5}{2}$

$y = - 2 x - 1$

$y = \frac{6 x}{2} + \frac{5}{2}$

$y = - 2 x - 1$

$y = \frac{6 x}{2} + \frac{5}{2}$

$y = - 2 x - 1$

Simplify the right side.

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x)}{2} + \frac{5}{2}$

$y = - 2 x - 1$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (3 x)}{2 (1)} + \frac{5}{2}$

$y = - 2 x - 1$

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot 1} + \frac{5}{2}$

$y = - 2 x - 1$

Rewrite the expression.

$y = \frac{3 x}{1} + \frac{5}{2}$

$y = - 2 x - 1$

Divide $3 x$ by $1$ .

$y = 3 x + \frac{5}{2}$

$y = - 2 x - 1$

$y = 3 x + \frac{5}{2}$

$y = - 2 x - 1$

$y = 3 x + \frac{5}{2}$

$y = - 2 x - 1$

$y = 3 x + \frac{5}{2}$

$y = - 2 x - 1$

$y = 3 x + \frac{5}{2}$

$y = - 2 x - 1$

Step 5

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

$(- \frac{7}{10}, \frac{2}{5})$

Step 6

Solve by Graphing 2x=-1-y , 2y=6x+5

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