Solve by Graphing x-3y=-12 2x-y=1

$x - 3 y = - 12$ $2 x - y = 1$

Step 1

Subtract $x$ from both sides of the equation.

$- 3 y = - 12 - x$

$2 x - y = 1$

Step 2

Divide each term in $- 3 y = - 12 - x$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 12 - x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 12}{- 3} + \frac{- x}{- 3}$

$2 x - y = 1$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 12}{- 3} + \frac{- x}{- 3}$

$2 x - y = 1$

Divide $y$ by $1$ .

$y = \frac{- 12}{- 3} + \frac{- x}{- 3}$

$2 x - y = 1$

$y = \frac{- 12}{- 3} + \frac{- x}{- 3}$

$2 x - y = 1$

$y = \frac{- 12}{- 3} + \frac{- x}{- 3}$

$2 x - y = 1$

Simplify the right side.

Simplify each term.

Divide $- 12$ by $- 3$ .

$y = 4 + \frac{- x}{- 3}$

$2 x - y = 1$

Dividing two negative values results in a positive value.

$y = 4 + \frac{x}{3}$

$2 x - y = 1$

$y = 4 + \frac{x}{3}$

$2 x - y = 1$

$y = 4 + \frac{x}{3}$

$2 x - y = 1$

$y = 4 + \frac{x}{3}$

$2 x - y = 1$

Step 3

Subtract $2 x$ from both sides of the equation.

$- y = 1 - 2 x$

$y = 4 + \frac{x}{3}$

Step 4

Divide each term in $- y = 1 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = 1 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{1}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 + \frac{x}{3}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{1}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 + \frac{x}{3}$

Divide $y$ by $1$ .

$y = \frac{1}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 + \frac{x}{3}$

$y = \frac{1}{- 1} + \frac{- 2 x}{- 1}$

$y = 4 + \frac{x}{3}$

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

$y = - 1 + \frac{- 2 x}{- 1}$

$y = 4 + \frac{x}{3}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y = - 1 - 1 \cdot (- 2 x)$

$y = 4 + \frac{x}{3}$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = - 1 - (- 2 x)$

$y = 4 + \frac{x}{3}$

Multiply $- 2$ by $- 1$ .

$y = - 1 + 2 x$

$y = 4 + \frac{x}{3}$

$y = - 1 + 2 x$

$y = 4 + \frac{x}{3}$

$y = - 1 + 2 x$

$y = 4 + \frac{x}{3}$

$y = - 1 + 2 x$

$y = 4 + \frac{x}{3}$

Step 5

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

$(3, 5)$

Step 6

Solve by Graphing x-3y=-12 2x-y=1

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