Solve by Substitution 2x+4y=-2 , 2x-y=4

$2 x + 4 y = - 2$ , $2 x - y = 4$

Step 1

Solve for $x$ in $2 x + 4 y = - 2$ .

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

$2 x = - 2 - 4 y$

$2 x - y = 4$

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

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

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

$2 x - y = 4$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$2 x - y = 4$

Divide $x$ by $1$ .

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

$2 x - y = 4$

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

$2 x - y = 4$

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

$2 x - y = 4$

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

$x = - 1 + \frac{- 4 y}{2}$

$2 x - y = 4$

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

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

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

$2 x - y = 4$

Cancel the common factors.

Factor $2$ out of $2$ .

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

$2 x - y = 4$

Cancel the common factor.

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

$2 x - y = 4$

Rewrite the expression.

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

$2 x - y = 4$

Divide $- 2 y$ by $1$ .

$x = - 1 - 2 y$

$2 x - y = 4$

$x = - 1 - 2 y$

$2 x - y = 4$

$x = - 1 - 2 y$

$2 x - y = 4$

$x = - 1 - 2 y$

$2 x - y = 4$

$x = - 1 - 2 y$

$2 x - y = 4$

$x = - 1 - 2 y$

$2 x - y = 4$

$x = - 1 - 2 y$

$2 x - y = 4$

Step 2

Replace all occurrences of $x$ with $- 1 - 2 y$ in each equation.

Replace all occurrences of $x$ in $2 x - y = 4$ with $- 1 - 2 y$ .

$2 (- 1 - 2 y) - y = 4$

$x = - 1 - 2 y$

Simplify the left side.

Simplify $2 (- 1 - 2 y) - y$ .

Simplify each term.

Apply the distributive property.

$2 \cdot - 1 + 2 (- 2 y) - y = 4$

$x = - 1 - 2 y$

Multiply $2$ by $- 1$ .

$- 2 + 2 (- 2 y) - y = 4$

$x = - 1 - 2 y$

Multiply $- 2$ by $2$ .

$- 2 - 4 y - y = 4$

$x = - 1 - 2 y$

$- 2 - 4 y - y = 4$

$x = - 1 - 2 y$

Subtract $y$ from $- 4 y$ .

$- 2 - 5 y = 4$

$x = - 1 - 2 y$

$- 2 - 5 y = 4$

$x = - 1 - 2 y$

$- 2 - 5 y = 4$

$x = - 1 - 2 y$

$- 2 - 5 y = 4$

$x = - 1 - 2 y$

Step 3

Solve for $y$ in $- 2 - 5 y = 4$ .

Move all terms not containing $y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$- 5 y = 4 + 2$

$x = - 1 - 2 y$

Add $4$ and $2$ .

$- 5 y = 6$

$x = - 1 - 2 y$

$- 5 y = 6$

$x = - 1 - 2 y$

Divide each term in $- 5 y = 6$ by $- 5$ and simplify.

Divide each term in $- 5 y = 6$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{6}{- 5}$

$x = - 1 - 2 y$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{6}{- 5}$

$x = - 1 - 2 y$

Divide $y$ by $1$ .

$y = \frac{6}{- 5}$

$x = - 1 - 2 y$

$y = \frac{6}{- 5}$

$x = - 1 - 2 y$

$y = \frac{6}{- 5}$

$x = - 1 - 2 y$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{6}{5}$

$x = - 1 - 2 y$

$y = - \frac{6}{5}$

$x = - 1 - 2 y$

$y = - \frac{6}{5}$

$x = - 1 - 2 y$

$y = - \frac{6}{5}$

$x = - 1 - 2 y$

Step 4

Replace all occurrences of $y$ with $- \frac{6}{5}$ in each equation.

Replace all occurrences of $y$ in $x = - 1 - 2 y$ with $- \frac{6}{5}$ .

$x = - 1 - 2 (- \frac{6}{5})$

$y = - \frac{6}{5}$

Simplify the right side.

Simplify $- 1 - 2 (- \frac{6}{5})$ .

Multiply $- 2 (- \frac{6}{5})$ .

Multiply $- 1$ by $- 2$ .

$x = - 1 + 2 (\frac{6}{5})$

$y = - \frac{6}{5}$

Combine $2$ and $\frac{6}{5}$ .

$x = - 1 + \frac{2 \cdot 6}{5}$

$y = - \frac{6}{5}$

Multiply $2$ by $6$ .

$x = - 1 + \frac{12}{5}$

$y = - \frac{6}{5}$

$x = - 1 + \frac{12}{5}$

$y = - \frac{6}{5}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - 1 \cdot \frac{5}{5} + \frac{12}{5}$

$y = - \frac{6}{5}$

Combine $- 1$ and $\frac{5}{5}$ .

$x = \frac{- 1 \cdot 5}{5} + \frac{12}{5}$

$y = - \frac{6}{5}$

Combine the numerators over the common denominator.

$x = \frac{- 1 \cdot 5 + 12}{5}$

$y = - \frac{6}{5}$

Simplify the numerator.

Multiply $- 1$ by $5$ .

$x = \frac{- 5 + 12}{5}$

$y = - \frac{6}{5}$

Add $- 5$ and $12$ .

$x = \frac{7}{5}$

$y = - \frac{6}{5}$

$x = \frac{7}{5}$

$y = - \frac{6}{5}$

$x = \frac{7}{5}$

$y = - \frac{6}{5}$

$x = \frac{7}{5}$

$y = - \frac{6}{5}$

$x = \frac{7}{5}$

$y = - \frac{6}{5}$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{7}{5}, - \frac{6}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{7}{5}, - \frac{6}{5})$

Equation Form:

$x = \frac{7}{5}, y = - \frac{6}{5}$

Step 7

Solve by Substitution 2x+4y=-2 , 2x-y=4

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