Solve the System of Equations 2x+y=-4 y=5/2x+5

$2 x + y = - 4$ $y = \frac{5}{2} x + 5$

Step 1

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

$y = - 4 - 2 x$

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

Step 2

Replace all occurrences of $y$ with $- 4 - 2 x$ in each equation.

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

$- 4 - 2 x = - 4 - 2 x$

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

Simplify the left side.

Remove parentheses.

$- 4 - 2 x = - 4 - 2 x$

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

$- 4 - 2 x = - 4 - 2 x$

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

Replace all occurrences of $y$ in $y = \frac{5}{2} x + 5$ with $- 4 - 2 x$ .

$- 4 - 2 x = \frac{5}{2} x + 5$

$- 4 - 2 x = - 4 - 2 x$

Simplify $- 4 - 2 x = \frac{5}{2} x + 5$ .

Simplify the left side.

Remove parentheses.

$- 4 - 2 x = \frac{5}{2} x + 5$

$- 4 - 2 x = - 4 - 2 x$

$- 4 - 2 x = \frac{5}{2} x + 5$

$- 4 - 2 x = - 4 - 2 x$

Simplify the right side.

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

$- 4 - 2 x = \frac{5 x}{2} + 5$

$- 4 - 2 x = - 4 - 2 x$

$- 4 - 2 x = \frac{5 x}{2} + 5$

$- 4 - 2 x = - 4 - 2 x$

$- 4 - 2 x = \frac{5 x}{2} + 5$

$- 4 - 2 x = - 4 - 2 x$

$- 4 - 2 x = \frac{5 x}{2} + 5$

$- 4 - 2 x = - 4 - 2 x$

Step 3

Remove any equations from the system that are always true.

$- 4 - 2 x = \frac{5 x}{2} + 5$

Step 4

Solve for $x$ in $- 4 - 2 x = \frac{5 x}{2} + 5$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $\frac{5 x}{2}$ from both sides of the equation.

$- 4 - 2 x - \frac{5 x}{2} = 5$

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

$- 4 - 2 x \cdot \frac{2}{2} - \frac{5 x}{2} = 5$

Combine $- 2 x$ and $\frac{2}{2}$ .

$- 4 + \frac{- 2 x \cdot 2}{2} - \frac{5 x}{2} = 5$

Combine the numerators over the common denominator.

$- 4 + \frac{- 2 x \cdot 2 - 5 x}{2} = 5$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 2 x \cdot 2 - 5 x$ .

Factor $x$ out of $- 2 x \cdot 2$ .

$- 4 + \frac{x (- 2 \cdot 2) - 5 x}{2} = 5$

Factor $x$ out of $- 5 x$ .

$- 4 + \frac{x (- 2 \cdot 2) + x \cdot - 5}{2} = 5$

Factor $x$ out of $x (- 2 \cdot 2) + x \cdot - 5$ .

$- 4 + \frac{x (- 2 \cdot 2 - 5)}{2} = 5$

$- 4 + \frac{x (- 2 \cdot 2 - 5)}{2} = 5$

Multiply $- 2$ by $2$ .

$- 4 + \frac{x (- 4 - 5)}{2} = 5$

Subtract $5$ from $- 4$ .

$- 4 + \frac{x \cdot - 9}{2} = 5$

$- 4 + \frac{x \cdot - 9}{2} = 5$

Move $- 9$ to the left of $x$ .

$- 4 + \frac{- 9 \cdot x}{2} = 5$

Move the negative in front of the fraction.

$- 4 - \frac{9 x}{2} = 5$

$- 4 - \frac{9 x}{2} = 5$

$- 4 - \frac{9 x}{2} = 5$

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

Add $4$ to both sides of the equation.

$- \frac{9 x}{2} = 5 + 4$

Add $5$ and $4$ .

$- \frac{9 x}{2} = 9$

$- \frac{9 x}{2} = 9$

Multiply both sides of the equation by $- \frac{2}{9}$ .

$- \frac{2}{9} (- \frac{9 x}{2}) = - \frac{2}{9} \cdot 9$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{9} (- \frac{9 x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$\frac{- 2}{9} (- \frac{9 x}{2}) = - \frac{2}{9} \cdot 9$

Move the leading negative in $- \frac{9 x}{2}$ into the numerator.

$\frac{- 2}{9} \cdot \frac{- 9 x}{2} = - \frac{2}{9} \cdot 9$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{9} \cdot \frac{- 9 x}{2} = - \frac{2}{9} \cdot 9$

Cancel the common factor.

$\frac{2 \cdot - 1}{9} \cdot \frac{- 9 x}{2} = - \frac{2}{9} \cdot 9$

Rewrite the expression.

$\frac{- 1}{9} (- 9 x) = - \frac{2}{9} \cdot 9$

$\frac{- 1}{9} (- 9 x) = - \frac{2}{9} \cdot 9$

Cancel the common factor of $9$ .

Factor $9$ out of $- 9 x$ .

$\frac{- 1}{9} (9 (- x)) = - \frac{2}{9} \cdot 9$

Cancel the common factor.

$\frac{- 1}{9} (9 (- x)) = - \frac{2}{9} \cdot 9$

Rewrite the expression.

$- - x = - \frac{2}{9} \cdot 9$

$- - x = - \frac{2}{9} \cdot 9$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{9} \cdot 9$

Multiply $x$ by $1$ .

$x = - \frac{2}{9} \cdot 9$

$x = - \frac{2}{9} \cdot 9$

$x = - \frac{2}{9} \cdot 9$

$x = - \frac{2}{9} \cdot 9$

Simplify the right side.

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{2}{9}$ into the numerator.

$x = \frac{- 2}{9} \cdot 9$

Cancel the common factor.

$x = \frac{- 2}{9} \cdot 9$

Rewrite the expression.

$x = - 2$

$x = - 2$

$x = - 2$

$x = - 2$

$x = - 2$

Step 5

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