Solve the System of Equations 2x-y=-15 2(x+3y)=-22

$2 x - y = - 15$ $2 (x + 3 y) = - 22$

Step 1

Solve for $x$ in $2 x - y = - 15$ .

Add $y$ to both sides of the equation.

$2 x = - 15 + y$

$2 (x + 3 y) = - 22$

Divide each term in $2 x = - 15 + y$ by $2$ and simplify.

Divide each term in $2 x = - 15 + y$ by $2$ .

$\frac{2 x}{2} = \frac{- 15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

Divide $x$ by $1$ .

$x = \frac{- 15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

$x = \frac{- 15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

$x = \frac{- 15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$2 (x + 3 y) = - 22$

Step 2

Replace all occurrences of $x$ with $- \frac{15}{2} + \frac{y}{2}$ in each equation.

Replace all occurrences of $x$ in $2 (x + 3 y) = - 22$ with $- \frac{15}{2} + \frac{y}{2}$ .

$2 ((- \frac{15}{2} + \frac{y}{2}) + 3 y) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Simplify the left side.

Simplify $2 ((- \frac{15}{2} + \frac{y}{2}) + 3 y)$ .

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

$2 (- \frac{15}{2} + \frac{y}{2} + 3 y \cdot \frac{2}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Combine $3 y$ and $\frac{2}{2}$ .

$2 (- \frac{15}{2} + \frac{y}{2} + \frac{3 y \cdot 2}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Combine the numerators over the common denominator.

$2 (- \frac{15}{2} + \frac{y + 3 y \cdot 2}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Combine the numerators over the common denominator.

$2 (\frac{- 15 + y + 3 y \cdot 2}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Multiply $2$ by $3$ .

$2 (\frac{- 15 + y + 6 y}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Add $y$ and $6 y$ .

$2 (\frac{- 15 + 7 y}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 (\frac{- 15 + 7 y}{2}) = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Rewrite the expression.

$- 15 + 7 y = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$- 15 + 7 y = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$- 15 + 7 y = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$- 15 + 7 y = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

$- 15 + 7 y = - 22$

$x = - \frac{15}{2} + \frac{y}{2}$

Step 3

Solve for $y$ in $- 15 + 7 y = - 22$ .

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

Add $15$ to both sides of the equation.

$7 y = - 22 + 15$

$x = - \frac{15}{2} + \frac{y}{2}$

Add $- 22$ and $15$ .

$7 y = - 7$

$x = - \frac{15}{2} + \frac{y}{2}$

$7 y = - 7$

$x = - \frac{15}{2} + \frac{y}{2}$

Divide each term in $7 y = - 7$ by $7$ and simplify.

Divide each term in $7 y = - 7$ by $7$ .

$\frac{7 y}{7} = \frac{- 7}{7}$

$x = - \frac{15}{2} + \frac{y}{2}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 7}{7}$

$x = - \frac{15}{2} + \frac{y}{2}$

Divide $y$ by $1$ .

$y = \frac{- 7}{7}$

$x = - \frac{15}{2} + \frac{y}{2}$

$y = \frac{- 7}{7}$

$x = - \frac{15}{2} + \frac{y}{2}$

$y = \frac{- 7}{7}$

$x = - \frac{15}{2} + \frac{y}{2}$

Simplify the right side.

Divide $- 7$ by $7$ .

$y = - 1$

$x = - \frac{15}{2} + \frac{y}{2}$

$y = - 1$

$x = - \frac{15}{2} + \frac{y}{2}$

$y = - 1$

$x = - \frac{15}{2} + \frac{y}{2}$

$y = - 1$

$x = - \frac{15}{2} + \frac{y}{2}$

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{15}{2} + \frac{y}{2}$ with $- 1$ .

$x = - \frac{15}{2} + \frac{- 1}{2}$

$y = - 1$

Simplify the right side.

Simplify $- \frac{15}{2} + \frac{- 1}{2}$ .

Combine the numerators over the common denominator.

$x = \frac{- 15 - 1}{2}$

$y = - 1$

Simplify the expression.

Subtract $1$ from $- 15$ .

$x = \frac{- 16}{2}$

$y = - 1$

Divide $- 16$ by $2$ .

$x = - 8$

$y = - 1$

$x = - 8$

$y = - 1$

$x = - 8$

$y = - 1$

$x = - 8$

$y = - 1$

$x = - 8$

$y = - 1$

Step 5

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

$(- 8, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 8, - 1)$

Equation Form:

$x = - 8, y = - 1$

Step 7

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