Solve by Graphing 2x-y=3 , 4x-2y=6

$2 x - y = 3$ , $4 x - 2 y = 6$

Step 1

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

$- y = 3 - 2 x$

$4 x - 2 y = 6$

Step 2

Divide each term in $- y = 3 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = 3 - 2 x$ by $- 1$ .

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

$4 x - 2 y = 6$

Simplify the left side.

Dividing two negative values results in a positive value.

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

$4 x - 2 y = 6$

Divide $y$ by $1$ .

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

$4 x - 2 y = 6$

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

$4 x - 2 y = 6$

Simplify the right side.

Simplify each term.

Divide $3$ by $- 1$ .

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

$4 x - 2 y = 6$

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

$y = - 3 - 1 \cdot (- 2 x)$

$4 x - 2 y = 6$

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

$y = - 3 - (- 2 x)$

$4 x - 2 y = 6$

Multiply $- 2$ by $- 1$ .

$y = - 3 + 2 x$

$4 x - 2 y = 6$

$y = - 3 + 2 x$

$4 x - 2 y = 6$

$y = - 3 + 2 x$

$4 x - 2 y = 6$

$y = - 3 + 2 x$

$4 x - 2 y = 6$

Step 3

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

$- 2 y = 6 - 4 x$

$y = - 3 + 2 x$

Step 4

Divide each term in $- 2 y = 6 - 4 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 6 - 4 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{- 4 x}{- 2}$

$y = - 3 + 2 x$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{- 4 x}{- 2}$

$y = - 3 + 2 x$

Divide $y$ by $1$ .

$y = \frac{6}{- 2} + \frac{- 4 x}{- 2}$

$y = - 3 + 2 x$

$y = \frac{6}{- 2} + \frac{- 4 x}{- 2}$

$y = - 3 + 2 x$

$y = \frac{6}{- 2} + \frac{- 4 x}{- 2}$

$y = - 3 + 2 x$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

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

$y = - 3 + 2 x$

Cancel the common factor of $- 4$ and $- 2$ .

Factor $- 2$ out of $- 4 x$ .

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

$y = - 3 + 2 x$

Cancel the common factors.

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

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

$y = - 3 + 2 x$

Cancel the common factor.

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

$y = - 3 + 2 x$

Rewrite the expression.

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

$y = - 3 + 2 x$

Divide $2 x$ by $1$ .

$y = - 3 + 2 x$

Step 5

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

$y = 2 x - 3$

Step 6

Solve by Graphing 2x-y=3 , 4x-2y=6

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