Solve by Substitution 2x+2y=-3 , 2x-y=5

$2 x + 2 y = - 3$ , $2 x - y = 5$

Step 1

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

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

$2 x = - 3 - 2 y$

$2 x - y = 5$

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

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

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

$2 x - y = 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

$2 x - y = 5$

Divide $x$ by $1$ .

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

$2 x - y = 5$

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

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

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

$2 x - y = 5$

Cancel the common factors.

Factor $2$ out of $2$ .

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

$2 x - y = 5$

Cancel the common factor.

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

$2 x - y = 5$

Rewrite the expression.

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

$2 x - y = 5$

Divide $- y$ by $1$ .

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

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

$2 x - y = 5$

Step 2

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

Replace all occurrences of $x$ in $2 x - y = 5$ with $- \frac{3}{2} - y$ .

$2 (- \frac{3}{2} - y) - y = 5$

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

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$2 (- \frac{3}{2}) + 2 (- y) - y = 5$

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

Cancel the common factor of $2$ .

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

$2 (\frac{- 3}{2}) + 2 (- y) - y = 5$

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

Cancel the common factor.

$2 (\frac{- 3}{2}) + 2 (- y) - y = 5$

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

Rewrite the expression.

$- 3 + 2 (- y) - y = 5$

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

$- 3 + 2 (- y) - y = 5$

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

Multiply $- 1$ by $2$ .

$- 3 - 2 y - y = 5$

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

$- 3 - 2 y - y = 5$

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

Subtract $y$ from $- 2 y$ .

$- 3 - 3 y = 5$

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

$- 3 - 3 y = 5$

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

$- 3 - 3 y = 5$

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

$- 3 - 3 y = 5$

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

Step 3

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

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

Add $3$ to both sides of the equation.

$- 3 y = 5 + 3$

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

Add $5$ and $3$ .

$- 3 y = 8$

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

$- 3 y = 8$

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

Divide each term in $- 3 y = 8$ by $- 3$ and simplify.

Divide each term in $- 3 y = 8$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{8}{- 3}$

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{8}{- 3}$

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

Divide $y$ by $1$ .

$y = \frac{8}{- 3}$

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

$y = \frac{8}{- 3}$

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

$y = \frac{8}{- 3}$

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

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

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

$y = - \frac{8}{3}$

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

$y = - \frac{8}{3}$

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

$y = - \frac{8}{3}$

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

Step 4

Replace all occurrences of $y$ with $- \frac{8}{3}$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{3}{2} - y$ with $- \frac{8}{3}$ .

$x = - \frac{3}{2} - (- \frac{8}{3})$

$y = - \frac{8}{3}$

Simplify the right side.

Simplify $- \frac{3}{2} - (- \frac{8}{3})$ .

Multiply $- (- \frac{8}{3})$ .

Multiply $- 1$ by $- 1$ .

$x = - \frac{3}{2} + 1 (\frac{8}{3})$

$y = - \frac{8}{3}$

Multiply $\frac{8}{3}$ by $1$ .

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

$y = - \frac{8}{3}$

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

$y = - \frac{8}{3}$

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

$y = - \frac{8}{3}$

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

$y = - \frac{8}{3}$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{3}{3}$ .

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

$y = - \frac{8}{3}$

Multiply $2$ by $3$ .

$x = - \frac{3 \cdot 3}{6} + \frac{8}{3} \cdot \frac{2}{2}$

$y = - \frac{8}{3}$

Multiply $\frac{8}{3}$ by $\frac{2}{2}$ .

$x = - \frac{3 \cdot 3}{6} + \frac{8 \cdot 2}{3 \cdot 2}$

$y = - \frac{8}{3}$

Multiply $3$ by $2$ .

$x = - \frac{3 \cdot 3}{6} + \frac{8 \cdot 2}{6}$

$y = - \frac{8}{3}$

$x = - \frac{3 \cdot 3}{6} + \frac{8 \cdot 2}{6}$

$y = - \frac{8}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 3 \cdot 3 + 8 \cdot 2}{6}$

$y = - \frac{8}{3}$

Simplify the numerator.

Multiply $- 3$ by $3$ .

$x = \frac{- 9 + 8 \cdot 2}{6}$

$y = - \frac{8}{3}$

Multiply $8$ by $2$ .

$x = \frac{- 9 + 16}{6}$

$y = - \frac{8}{3}$

Add $- 9$ and $16$ .

$x = \frac{7}{6}$

$y = - \frac{8}{3}$

$x = \frac{7}{6}$

$y = - \frac{8}{3}$

$x = \frac{7}{6}$

$y = - \frac{8}{3}$

$x = \frac{7}{6}$

$y = - \frac{8}{3}$

$x = \frac{7}{6}$

$y = - \frac{8}{3}$

Step 5

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

$(\frac{7}{6}, - \frac{8}{3})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{7}{6}, - \frac{8}{3})$

Equation Form:

$x = \frac{7}{6}, y = - \frac{8}{3}$

Step 7

Solve by Substitution 2x+2y=-3 , 2x-y=5

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