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

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

Step 1

Subtract $x$ from both sides of the equation.

$- 3 y = - 3 - x$

$- x + 3 y = 3$

Step 2

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

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

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

$- x + 3 y = 3$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$- x + 3 y = 3$

Divide $y$ by $1$ .

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

$- x + 3 y = 3$

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

$- x + 3 y = 3$

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

$- x + 3 y = 3$

Simplify the right side.

Simplify each term.

Divide $- 3$ by $- 3$ .

$y = 1 + \frac{- x}{- 3}$

$- x + 3 y = 3$

Dividing two negative values results in a positive value.

$y = 1 + \frac{x}{3}$

$- x + 3 y = 3$

$y = 1 + \frac{x}{3}$

$- x + 3 y = 3$

$y = 1 + \frac{x}{3}$

$- x + 3 y = 3$

$y = 1 + \frac{x}{3}$

$- x + 3 y = 3$

Step 3

Add $x$ to both sides of the equation.

$3 y = 3 + x$

$y = 1 + \frac{x}{3}$

Step 4

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

Divide each term in $3 y = 3 + x$ by $3$ .

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

$y = 1 + \frac{x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$y = 1 + \frac{x}{3}$

Divide $y$ by $1$ .

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

$y = 1 + \frac{x}{3}$

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

$y = 1 + \frac{x}{3}$

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

$y = 1 + \frac{x}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$y = 1 + \frac{x}{3}$

Step 5

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

$y = \frac{x}{3} + 1$

Step 6

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

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