Solve by Graphing x-y=1 , x+y=3

$x - y = 1$ , $x + y = 3$

Step 1

Subtract $x$ from both sides of the equation.

$- y = 1 - x$

$x + y = 3$

Step 2

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

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

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

$x + y = 3$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$x + y = 3$

Divide $y$ by $1$ .

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

$x + y = 3$

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

$x + y = 3$

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

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

$x + y = 3$

Dividing two negative values results in a positive value.

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

$x + y = 3$

Divide $x$ by $1$ .

$y = - 1 + x$

$x + y = 3$

$y = - 1 + x$

$x + y = 3$

$y = - 1 + x$

$x + y = 3$

$y = - 1 + x$

$x + y = 3$

Step 3

Subtract $x$ from both sides of the equation.

$y = 3 - x$

$y = - 1 + x$

Step 4

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

$(2, 1)$

Step 5