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

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

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

$y = 5 - 2 x$

$x - 3 y = - 8$

Subtract $x$ from both sides of the equation.

$- 3 y = - 8 - x$

$y = 5 - 2 x$

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.

Simplify each term.

Dividing two negative values results in a positive value.

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

$y = 5 - 2 x$

Dividing two negative values results in a positive value.

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

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

$y = 5 - 2 x$

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

$(1, 3)$