Solve by Substitution r+s=-12 4r-6s=12

$r + s = - 12$ $4 r - 6 s = 12$

Step 1

Subtract $s$ from both sides of the equation.

$r = - 12 - s$

$4 r - 6 s = 12$

Step 2

Replace all occurrences of $r$ with $- 12 - s$ in each equation.

Replace all occurrences of $r$ in $4 r - 6 s = 12$ with $- 12 - s$ .

$4 (- 12 - s) - 6 s = 12$

$r = - 12 - s$

Simplify the left side.

Simplify $4 (- 12 - s) - 6 s$ .

Simplify each term.

Apply the distributive property.

$4 \cdot - 12 + 4 (- s) - 6 s = 12$

$r = - 12 - s$

Multiply $4$ by $- 12$ .

$- 48 + 4 (- s) - 6 s = 12$

$r = - 12 - s$

Multiply $- 1$ by $4$ .

$- 48 - 4 s - 6 s = 12$

$r = - 12 - s$

$- 48 - 4 s - 6 s = 12$

$r = - 12 - s$

Subtract $6 s$ from $- 4 s$ .

$- 48 - 10 s = 12$

$r = - 12 - s$

$- 48 - 10 s = 12$

$r = - 12 - s$

$- 48 - 10 s = 12$

$r = - 12 - s$

$- 48 - 10 s = 12$

$r = - 12 - s$

Step 3

Solve for $s$ in $- 48 - 10 s = 12$ .

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

Add $48$ to both sides of the equation.

$- 10 s = 12 + 48$

$r = - 12 - s$

Add $12$ and $48$ .

$- 10 s = 60$

$r = - 12 - s$

$- 10 s = 60$

$r = - 12 - s$

Divide each term in $- 10 s = 60$ by $- 10$ and simplify.

Divide each term in $- 10 s = 60$ by $- 10$ .

$\frac{- 10 s}{- 10} = \frac{60}{- 10}$

$r = - 12 - s$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 s}{- 10} = \frac{60}{- 10}$

$r = - 12 - s$

Divide $s$ by $1$ .

$s = \frac{60}{- 10}$

$r = - 12 - s$

$s = \frac{60}{- 10}$

$r = - 12 - s$

$s = \frac{60}{- 10}$

$r = - 12 - s$

Simplify the right side.

Divide $60$ by $- 10$ .

$s = - 6$

$r = - 12 - s$

$s = - 6$

$r = - 12 - s$

$s = - 6$

$r = - 12 - s$

$s = - 6$

$r = - 12 - s$

Step 4

Replace all occurrences of $s$ with $- 6$ in each equation.

Replace all occurrences of $s$ in $r = - 12 - s$ with $- 6$ .

$r = - 12 - (- 6)$

$s = - 6$

Simplify the right side.

Simplify $- 12 - (- 6)$ .

Multiply $- 1$ by $- 6$ .

$r = - 12 + 6$

$s = - 6$

Add $- 12$ and $6$ .

$r = - 6$

$s = - 6$

$r = - 6$

$s = - 6$

$r = - 6$

$s = - 6$

$r = - 6$

$s = - 6$

Step 5

List all of the solutions.

$r = - 6, s = - 6$

Solve by Substitution r+s=-12 4r-6s=12

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