Solve by Graphing x+3y=6 -x-3y=6

$x + 3 y = 6$ $- x - 3 y = 6$

Step 1

Subtract $x$ from both sides of the equation.

$3 y = 6 - x$

$- x - 3 y = 6$

Step 2

Divide each term in $3 y = 6 - x$ by $3$ and simplify.

Divide each term in $3 y = 6 - x$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3} + \frac{- x}{3}$

$- x - 3 y = 6$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3} + \frac{- x}{3}$

$- x - 3 y = 6$

Divide $y$ by $1$ .

$y = \frac{6}{3} + \frac{- x}{3}$

$- x - 3 y = 6$

$y = \frac{6}{3} + \frac{- x}{3}$

$- x - 3 y = 6$

$y = \frac{6}{3} + \frac{- x}{3}$

$- x - 3 y = 6$

Simplify the right side.

Simplify each term.

Divide $6$ by $3$ .

$y = 2 + \frac{- x}{3}$

$- x - 3 y = 6$

Move the negative in front of the fraction.

$y = 2 - \frac{x}{3}$

$- x - 3 y = 6$

$y = 2 - \frac{x}{3}$

$- x - 3 y = 6$

$y = 2 - \frac{x}{3}$

$- x - 3 y = 6$

$y = 2 - \frac{x}{3}$

$- x - 3 y = 6$

Step 3

Add $x$ to both sides of the equation.

$- 3 y = 6 + x$

$y = 2 - \frac{x}{3}$

Step 4

Divide each term in $- 3 y = 6 + x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 6 + x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{6}{- 3} + \frac{x}{- 3}$

$y = 2 - \frac{x}{3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{6}{- 3} + \frac{x}{- 3}$

$y = 2 - \frac{x}{3}$

Divide $y$ by $1$ .

$y = \frac{6}{- 3} + \frac{x}{- 3}$

$y = 2 - \frac{x}{3}$

$y = \frac{6}{- 3} + \frac{x}{- 3}$

$y = 2 - \frac{x}{3}$

$y = \frac{6}{- 3} + \frac{x}{- 3}$

$y = 2 - \frac{x}{3}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 3$ .

$y = - 2 + \frac{x}{- 3}$

$y = 2 - \frac{x}{3}$

Move the negative in front of the fraction.

$y = - 2 - \frac{x}{3}$

$y = 2 - \frac{x}{3}$

$y = - 2 - \frac{x}{3}$

$y = 2 - \frac{x}{3}$

$y = - 2 - \frac{x}{3}$

$y = 2 - \frac{x}{3}$

$y = - 2 - \frac{x}{3}$

$y = 2 - \frac{x}{3}$

Step 5

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

No solution

Step 6

Solve by Graphing x+3y=6 -x-3y=6

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