Solve by Graphing 6x-2y=12 , 3x=y+6

$6 x - 2 y = 12$ , $3 x = y + 6$

Step 1

Subtract $6 x$ from both sides of the equation.

$- 2 y = 12 - 6 x$

$3 x = y + 6$

Step 2

Divide each term in $- 2 y = 12 - 6 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 12 - 6 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

$3 x = y + 6$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

$3 x = y + 6$

Divide $y$ by $1$ .

$y = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

$3 x = y + 6$

$y = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

$3 x = y + 6$

$y = \frac{12}{- 2} + \frac{- 6 x}{- 2}$

$3 x = y + 6$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 2$ .

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

$3 x = y + 6$

Cancel the common factor of $- 6$ and $- 2$ .

Factor $- 2$ out of $- 6 x$ .

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

$3 x = y + 6$

Cancel the common factors.

Factor $- 2$ out of $- 2$ .

$y = - 6 + \frac{- 2 (3 x)}{- 2 \cdot 1}$

$3 x = y + 6$

Cancel the common factor.

$y = - 6 + \frac{- 2 (3 x)}{- 2 \cdot 1}$

$3 x = y + 6$

Rewrite the expression.

$y = - 6 + \frac{3 x}{1}$

$3 x = y + 6$

Divide $3 x$ by $1$ .

$y = - 6 + 3 x$

$3 x = y + 6$

$y = - 6 + 3 x$

$3 x = y + 6$

$y = - 6 + 3 x$

$3 x = y + 6$

$y = - 6 + 3 x$

$3 x = y + 6$

$y = - 6 + 3 x$

$3 x = y + 6$

$y = - 6 + 3 x$

$3 x = y + 6$

Step 3

Rewrite the equation as $y + 6 = 3 x$ .

$y + 6 = 3 x$

$y = - 6 + 3 x$

Step 4

Subtract $6$ from both sides of the equation.

$y = 3 x - 6$

$y = - 6 + 3 x$

Step 5

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

Always true

Step 6

Solve by Graphing 6x-2y=12 , 3x=y+6

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