Solve by Graphing x+y=6 , x-y=0

$x + y = 6$ , $x - y = 0$

Step 1

Subtract $x$ from both sides of the equation.

$y = 6 - x$

$x - y = 0$

Step 2

Subtract $x$ from both sides of the equation.

$- y = - x$

$y = 6 - x$

Step 3

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

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

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

$y = 6 - x$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$y = 6 - x$

Divide $y$ by $1$ .

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

$y = 6 - x$

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

$y = 6 - x$

Simplify the right side.

Dividing two negative values results in a positive value.

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

$y = 6 - x$

Divide $x$ by $1$ .

$y = x$

$y = 6 - x$

$y = x$

$y = 6 - x$

$y = x$

$y = 6 - x$

Step 4

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

$(3, 3)$

Step 5