Solve by Substitution 2x+4y=-3 , 2x-y=7

$2 x + 4 y = - 3$ , $2 x - y = 7$

Step 1

Solve for $x$ in $2 x + 4 y = - 3$ .

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

$2 x = - 3 - 4 y$

$2 x - y = 7$

Divide each term in $2 x = - 3 - 4 y$ by $2$ and simplify.

Divide each term in $2 x = - 3 - 4 y$ by $2$ .

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

$2 x - y = 7$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$2 x - y = 7$

Divide $x$ by $1$ .

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

$2 x - y = 7$

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

$2 x - y = 7$

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

$2 x - y = 7$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$2 x - y = 7$

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

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

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

$2 x - y = 7$

Cancel the common factors.

Factor $2$ out of $2$ .

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

$2 x - y = 7$

Cancel the common factor.

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

$2 x - y = 7$

Rewrite the expression.

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

$2 x - y = 7$

Divide $- 2 y$ by $1$ .

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

$2 x - y = 7$

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

$2 x - y = 7$

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

$2 x - y = 7$

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

$2 x - y = 7$

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

$2 x - y = 7$

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

$2 x - y = 7$

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

$2 x - y = 7$

Step 2

Replace all occurrences of $x$ with $- \frac{3}{2} - 2 y$ in each equation.

Replace all occurrences of $x$ in $2 x - y = 7$ with $- \frac{3}{2} - 2 y$ .

$2 (- \frac{3}{2} - 2 y) - y = 7$

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

Simplify the left side.

Simplify $2 (- \frac{3}{2} - 2 y) - y$ .

Simplify each term.

Apply the distributive property.

$2 (- \frac{3}{2}) + 2 (- 2 y) - y = 7$

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$2 (\frac{- 3}{2}) + 2 (- 2 y) - y = 7$

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

Cancel the common factor.

$2 (\frac{- 3}{2}) + 2 (- 2 y) - y = 7$

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

Rewrite the expression.

$- 3 + 2 (- 2 y) - y = 7$

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

$- 3 + 2 (- 2 y) - y = 7$

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

Multiply $- 2$ by $2$ .

$- 3 - 4 y - y = 7$

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

$- 3 - 4 y - y = 7$

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

Subtract $y$ from $- 4 y$ .

$- 3 - 5 y = 7$

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

$- 3 - 5 y = 7$

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

$- 3 - 5 y = 7$

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

$- 3 - 5 y = 7$

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

Step 3

Solve for $y$ in $- 3 - 5 y = 7$ .

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

Add $3$ to both sides of the equation.

$- 5 y = 7 + 3$

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

Add $7$ and $3$ .

$- 5 y = 10$

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

$- 5 y = 10$

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

Divide each term in $- 5 y = 10$ by $- 5$ and simplify.

Divide each term in $- 5 y = 10$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{10}{- 5}$

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{10}{- 5}$

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

Divide $y$ by $1$ .

$y = \frac{10}{- 5}$

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

$y = \frac{10}{- 5}$

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

$y = \frac{10}{- 5}$

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

Simplify the right side.

Divide $10$ by $- 5$ .

$y = - 2$

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

$y = - 2$

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

$y = - 2$

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

$y = - 2$

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

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{3}{2} - 2 y$ with $- 2$ .

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

$y = - 2$

Simplify the right side.

Simplify $- \frac{3}{2} - 2 \cdot - 2$ .

Multiply $- 2$ by $- 2$ .

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

$y = - 2$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

$y = - 2$

Combine $4$ and $\frac{2}{2}$ .

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

$y = - 2$

Combine the numerators over the common denominator.

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

$y = - 2$

Simplify the numerator.

Multiply $4$ by $2$ .

$x = \frac{- 3 + 8}{2}$

$y = - 2$

Add $- 3$ and $8$ .

$x = \frac{5}{2}$

$y = - 2$

$x = \frac{5}{2}$

$y = - 2$

$x = \frac{5}{2}$

$y = - 2$

$x = \frac{5}{2}$

$y = - 2$

$x = \frac{5}{2}$

$y = - 2$

Step 5

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

$(\frac{5}{2}, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{5}{2}, - 2)$

Equation Form:

$x = \frac{5}{2}, y = - 2$

Step 7

Solve by Substitution 2x+4y=-3 , 2x-y=7

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