Solve by Graphing -2x-y=-5 2x-3y=1

$- 2 x - y = - 5$ $2 x - 3 y = 1$

Step 1

Add $2 x$ to both sides of the equation.

$- y = - 5 + 2 x$

$2 x - 3 y = 1$

Step 2

Divide each term in $- y = - 5 + 2 x$ by $- 1$ and simplify.

Divide each term in $- y = - 5 + 2 x$ by $- 1$ .

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

$2 x - 3 y = 1$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$2 x - 3 y = 1$

Divide $y$ by $1$ .

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

$2 x - 3 y = 1$

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

$2 x - 3 y = 1$

Simplify the right side.

Simplify each term.

Divide $- 5$ by $- 1$ .

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

$2 x - 3 y = 1$

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

$y = 5 - 1 \cdot (2 x)$

$2 x - 3 y = 1$

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

$y = 5 - (2 x)$

$2 x - 3 y = 1$

Multiply $2$ by $- 1$ .

$y = 5 - 2 x$

$2 x - 3 y = 1$

$y = 5 - 2 x$

$2 x - 3 y = 1$

$y = 5 - 2 x$

$2 x - 3 y = 1$

$y = 5 - 2 x$

$2 x - 3 y = 1$

Step 3

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

$- 3 y = 1 - 2 x$

$y = 5 - 2 x$

Step 4

Divide each term in $- 3 y = 1 - 2 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 1 - 2 x$ by $- 3$ .

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

$y = 5 - 2 x$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = 5 - 2 x$

Divide $y$ by $1$ .

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$y = 5 - 2 x$

Dividing two negative values results in a positive value.

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

Step 5

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

$(2, 1)$

Step 6

Solve by Graphing -2x-y=-5 2x-3y=1

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