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

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

Step 1

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

$- y = 6 - 2 x$

$6 x - 3 y = 6$

Step 2

Divide each term in $- y = 6 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = 6 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{- 2 x}{- 1}$

$6 x - 3 y = 6$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{- 2 x}{- 1}$

$6 x - 3 y = 6$

Divide $y$ by $1$ .

$y = \frac{6}{- 1} + \frac{- 2 x}{- 1}$

$6 x - 3 y = 6$

$y = \frac{6}{- 1} + \frac{- 2 x}{- 1}$

$6 x - 3 y = 6$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 1$ .

$y = - 6 + \frac{- 2 x}{- 1}$

$6 x - 3 y = 6$

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

$y = - 6 - 1 \cdot (- 2 x)$

$6 x - 3 y = 6$

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

$y = - 6 - (- 2 x)$

$6 x - 3 y = 6$

Multiply $- 2$ by $- 1$ .

$y = - 6 + 2 x$

$6 x - 3 y = 6$

$y = - 6 + 2 x$

$6 x - 3 y = 6$

$y = - 6 + 2 x$

$6 x - 3 y = 6$

$y = - 6 + 2 x$

$6 x - 3 y = 6$

Step 3

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

$- 3 y = 6 - 6 x$

$y = - 6 + 2 x$

Step 4

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

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

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

$y = - 6 + 2 x$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = - 6 + 2 x$

Divide $y$ by $1$ .

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

$y = - 6 + 2 x$

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

$y = - 6 + 2 x$

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

$y = - 6 + 2 x$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 3$ .

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

$y = - 6 + 2 x$

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

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

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

$y = - 6 + 2 x$

Cancel the common factors.

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

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

$y = - 6 + 2 x$

Cancel the common factor.

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

$y = - 6 + 2 x$

Rewrite the expression.

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

$y = - 6 + 2 x$

Divide $2 x$ by $1$ .

$y = - 2 + 2 x$

$y = - 6 + 2 x$

$y = - 2 + 2 x$

$y = - 6 + 2 x$

$y = - 2 + 2 x$

$y = - 6 + 2 x$

$y = - 2 + 2 x$

$y = - 6 + 2 x$

$y = - 2 + 2 x$

$y = - 6 + 2 x$

$y = - 2 + 2 x$

$y = - 6 + 2 x$

Step 5

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

No solution

Step 6

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

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