Solve by Graphing x-3y=6 , 4x-12y=24

$x - 3 y = 6$ , $4 x - 12 y = 24$

Step 1

Subtract $x$ from both sides of the equation.

$- 3 y = 6 - x$

$4 x - 12 y = 24$

Step 2

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

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

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

$4 x - 12 y = 24$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$4 x - 12 y = 24$

Divide $y$ by $1$ .

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

$4 x - 12 y = 24$

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

$4 x - 12 y = 24$

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

$4 x - 12 y = 24$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 3$ .

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

$4 x - 12 y = 24$

Dividing two negative values results in a positive value.

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

$4 x - 12 y = 24$

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

$4 x - 12 y = 24$

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

$4 x - 12 y = 24$

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

$4 x - 12 y = 24$

Step 3

Subtract $4 x$ from both sides of the equation.

$- 12 y = 24 - 4 x$

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

Step 4

Divide each term in $- 12 y = 24 - 4 x$ by $- 12$ and simplify.

Divide each term in $- 12 y = 24 - 4 x$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{24}{- 12} + \frac{- 4 x}{- 12}$

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

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{24}{- 12} + \frac{- 4 x}{- 12}$

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

Divide $y$ by $1$ .

$y = \frac{24}{- 12} + \frac{- 4 x}{- 12}$

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

$y = \frac{24}{- 12} + \frac{- 4 x}{- 12}$

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

$y = \frac{24}{- 12} + \frac{- 4 x}{- 12}$

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

Simplify the right side.

Simplify each term.

Divide $24$ by $- 12$ .

$y = - 2 + \frac{- 4 x}{- 12}$

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

Cancel the common factor of $- 4$ and $- 12$ .

Factor $- 4$ out of $- 4 x$ .

$y = - 2 + \frac{- 4 x}{- 12}$

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

Cancel the common factors.

Factor $- 4$ out of $- 12$ .

$y = - 2 + \frac{- 4 x}{- 4 \cdot 3}$

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

Cancel the common factor.

$y = - 2 + \frac{- 4 x}{- 4 \cdot 3}$

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

Rewrite the expression.

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

Step 5

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

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

Step 6

Solve by Graphing x-3y=6 , 4x-12y=24

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