Solve by Substitution 3x+5y=-27 , 4x+2y=-22

$3 x + 5 y = - 27$ , $4 x + 2 y = - 22$

Step 1

Solve for $x$ in $3 x + 5 y = - 27$ .

Subtract $5 y$ from both sides of the equation.

$3 x = - 27 - 5 y$

$4 x + 2 y = - 22$

Divide each term in $3 x = - 27 - 5 y$ by $3$ and simplify.

Divide each term in $3 x = - 27 - 5 y$ by $3$ .

$\frac{3 x}{3} = \frac{- 27}{3} + \frac{- 5 y}{3}$

$4 x + 2 y = - 22$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 27}{3} + \frac{- 5 y}{3}$

$4 x + 2 y = - 22$

Divide $x$ by $1$ .

$x = \frac{- 27}{3} + \frac{- 5 y}{3}$

$4 x + 2 y = - 22$

$x = \frac{- 27}{3} + \frac{- 5 y}{3}$

$4 x + 2 y = - 22$

$x = \frac{- 27}{3} + \frac{- 5 y}{3}$

$4 x + 2 y = - 22$

Simplify the right side.

Simplify each term.

Divide $- 27$ by $3$ .

$x = - 9 + \frac{- 5 y}{3}$

$4 x + 2 y = - 22$

Move the negative in front of the fraction.

$x = - 9 - \frac{5 y}{3}$

$4 x + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

$4 x + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

$4 x + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

$4 x + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

$4 x + 2 y = - 22$

Step 2

Replace all occurrences of $x$ with $- 9 - \frac{5 y}{3}$ in each equation.

Replace all occurrences of $x$ in $4 x + 2 y = - 22$ with $- 9 - \frac{5 y}{3}$ .

$4 (- 9 - \frac{5 y}{3}) + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

Simplify the left side.

Simplify $4 (- 9 - \frac{5 y}{3}) + 2 y$ .

Simplify each term.

Apply the distributive property.

$4 \cdot - 9 + 4 (- \frac{5 y}{3}) + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

Multiply $4$ by $- 9$ .

$- 36 + 4 (- \frac{5 y}{3}) + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

Multiply $4 (- \frac{5 y}{3})$ .

Multiply $- 1$ by $4$ .

$- 36 - 4 \frac{5 y}{3} + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

Combine $- 4$ and $\frac{5 y}{3}$ .

$- 36 + \frac{- 4 (5 y)}{3} + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

Multiply $5$ by $- 4$ .

$- 36 + \frac{- 20 y}{3} + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

$- 36 + \frac{- 20 y}{3} + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

Move the negative in front of the fraction.

$- 36 - \frac{20 y}{3} + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

$- 36 - \frac{20 y}{3} + 2 y = - 22$

$x = - 9 - \frac{5 y}{3}$

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

$- 36 - \frac{20 y}{3} + 2 y \cdot \frac{3}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Simplify terms.

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

$- 36 - \frac{20 y}{3} + \frac{2 y \cdot 3}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Combine the numerators over the common denominator.

$- 36 + \frac{- 20 y + 2 y \cdot 3}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

$- 36 + \frac{- 20 y + 2 y \cdot 3}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Simplify each term.

Simplify the numerator.

Factor $2 y$ out of $- 20 y + 2 y \cdot 3$ .

Factor $2 y$ out of $- 20 y$ .

$- 36 + \frac{2 y (- 10) + 2 y \cdot 3}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Factor $2 y$ out of $2 y \cdot 3$ .

$- 36 + \frac{2 y (- 10) + 2 y (3)}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Factor $2 y$ out of $2 y (- 10) + 2 y (3)$ .

$- 36 + \frac{2 y (- 10 + 3)}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

$- 36 + \frac{2 y (- 10 + 3)}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Add $- 10$ and $3$ .

$- 36 + \frac{2 y \cdot - 7}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Multiply $- 7$ by $2$ .

$- 36 + \frac{- 14 y}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

$- 36 + \frac{- 14 y}{3} = - 22$

$x = - 9 - \frac{5 y}{3}$

Move the negative in front of the fraction.