Solve by Graphing x-2y=2 x+y=5

$x - 2 y = 2$ $x + y = 5$

Step 1

Subtract $x$ from both sides of the equation.

$- 2 y = 2 - x$

$x + y = 5$

Step 2

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

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

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

$x + y = 5$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$x + y = 5$

Divide $y$ by $1$ .

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

$x + y = 5$

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

$x + y = 5$

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

$x + y = 5$

Simplify the right side.

Simplify each term.

Divide $2$ by $- 2$ .

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

$x + y = 5$

Dividing two negative values results in a positive value.

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

$x + y = 5$

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

$x + y = 5$

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

$x + y = 5$

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

$x + y = 5$

Step 3

Subtract $x$ from both sides of the equation.

$y = 5 - x$

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

Step 4

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

$(4, 1)$

Step 5