Solve by Graphing -2x+y=5 ; x+3y=8

$- 2 x + y = 5$ ; $x + 3 y = 8$

Step 1

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

$y = 5 + 2 x$

$x + 3 y = 8$

Step 2

Subtract $x$ from both sides of the equation.

$3 y = 8 - x$

$y = 5 + 2 x$

Step 3

Divide each term in $3 y = 8 - x$ by $3$ and simplify.

Divide each term in $3 y = 8 - x$ by $3$ .

$\frac{3 y}{3} = \frac{8}{3} + \frac{- x}{3}$

$y = 5 + 2 x$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{8}{3} + \frac{- x}{3}$

$y = 5 + 2 x$

Divide $y$ by $1$ .

$y = \frac{8}{3} + \frac{- x}{3}$

$y = 5 + 2 x$

$y = \frac{8}{3} + \frac{- x}{3}$

$y = 5 + 2 x$

$y = \frac{8}{3} + \frac{- x}{3}$

$y = 5 + 2 x$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{8}{3} - \frac{x}{3}$

$y = 5 + 2 x$

$y = \frac{8}{3} - \frac{x}{3}$

$y = 5 + 2 x$

$y = \frac{8}{3} - \frac{x}{3}$

$y = 5 + 2 x$

Step 4

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

$(- 1, 3)$

Step 5