Solve by Graphing 3x-6y=12 , 9x+18y=36

$3 x - 6 y = 12$ , $9 x + 18 y = 36$

Step 1

Subtract $3 x$ from both sides of the equation.

$- 6 y = 12 - 3 x$

$9 x + 18 y = 36$

Step 2

Divide each term in $- 6 y = 12 - 3 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 12 - 3 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{12}{- 6} + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

Divide $y$ by $1$ .

$y = \frac{12}{- 6} + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

$y = \frac{12}{- 6} + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

$y = \frac{12}{- 6} + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 6$ .

$y = - 2 + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

Cancel the common factor of $- 3$ and $- 6$ .

Factor $- 3$ out of $- 3 x$ .

$y = - 2 + \frac{- 3 x}{- 6}$

$9 x + 18 y = 36$

Cancel the common factors.

Factor $- 3$ out of $- 6$ .

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

$9 x + 18 y = 36$

Cancel the common factor.

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

$9 x + 18 y = 36$

Rewrite the expression.

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

$9 x + 18 y = 36$

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

$9 x + 18 y = 36$

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

$9 x + 18 y = 36$

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

$9 x + 18 y = 36$

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

$9 x + 18 y = 36$

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

$9 x + 18 y = 36$

Step 3

Subtract $9 x$ from both sides of the equation.

$18 y = 36 - 9 x$

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

Step 4

Divide each term in $18 y = 36 - 9 x$ by $18$ and simplify.

Divide each term in $18 y = 36 - 9 x$ by $18$ .

$\frac{18 y}{18} = \frac{36}{18} + \frac{- 9 x}{18}$

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

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 y}{18} = \frac{36}{18} + \frac{- 9 x}{18}$

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

Divide $y$ by $1$ .

$y = \frac{36}{18} + \frac{- 9 x}{18}$

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

$y = \frac{36}{18} + \frac{- 9 x}{18}$

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

$y = \frac{36}{18} + \frac{- 9 x}{18}$

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

Simplify the right side.

Simplify each term.

Divide $36$ by $18$ .

$y = 2 + \frac{- 9 x}{18}$

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

Cancel the common factor of $- 9$ and $18$ .

Factor $9$ out of $- 9 x$ .

$y = 2 + \frac{9 (- x)}{18}$

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

Cancel the common factors.

Factor $9$ out of $18$ .

$y = 2 + \frac{9 (- x)}{9 (2)}$

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

Cancel the common factor.

$y = 2 + \frac{9 (- x)}{9 \cdot 2}$

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

Rewrite the expression.

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 5

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

$(4, 0)$

Step 6

Solve by Graphing 3x-6y=12 , 9x+18y=36

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