Solve by Graphing x-3y=6 y=2x+3

$x - 3 y = 6$ $y = 2 x + 3$

Step 1

Subtract $x$ from both sides of the equation.

$- 3 y = 6 - x$

$y = 2 x + 3$

Step 2

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

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

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

$y = 2 x + 3$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = 2 x + 3$

Divide $y$ by $1$ .

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

$y = 2 x + 3$

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

$y = 2 x + 3$

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

$y = 2 x + 3$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 3$ .

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

$y = 2 x + 3$

Dividing two negative values results in a positive value.

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

$y = 2 x + 3$

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

$y = 2 x + 3$

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

$y = 2 x + 3$

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

$y = 2 x + 3$

Step 3

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

$(- 3, - 3)$

Step 4