Solve the System of Equations 9r+q=13 3r+2q=-4

$9 r + q = 13$ $3 r + 2 q = - 4$

Subtract $9 r$ from both sides of the equation.

$q = 13 - 9 r$

$3 r + 2 q = - 4$

Replace all occurrences of $q$ with $13 - 9 r$ in each equation.

Replace all occurrences of $q$ in $3 r + 2 q = - 4$ with $13 - 9 r$ .

$3 r + 2 (13 - 9 r) = - 4$

$q = 13 - 9 r$

Simplify the left side.

Simplify $3 r + 2 (13 - 9 r)$ .

Simplify each term.

Apply the distributive property.

$3 r + 2 \cdot 13 + 2 (- 9 r) = - 4$

$q = 13 - 9 r$

Multiply $2$ by $13$ .

$3 r + 26 + 2 (- 9 r) = - 4$

$q = 13 - 9 r$

Multiply $- 9$ by $2$ .

$3 r + 26 - 18 r = - 4$

$q = 13 - 9 r$

$3 r + 26 - 18 r = - 4$

$q = 13 - 9 r$

Subtract $18 r$ from $3 r$ .

$- 15 r + 26 = - 4$

$q = 13 - 9 r$

$- 15 r + 26 = - 4$

$q = 13 - 9 r$

$- 15 r + 26 = - 4$

$q = 13 - 9 r$

$- 15 r + 26 = - 4$

$q = 13 - 9 r$

Solve for $r$ in $- 15 r + 26 = - 4$ .

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

Subtract $26$ from both sides of the equation.

$- 15 r = - 4 - 26$

$q = 13 - 9 r$

Subtract $26$ from $- 4$ .

$- 15 r = - 30$

$q = 13 - 9 r$

$- 15 r = - 30$

$q = 13 - 9 r$

Divide each term in $- 15 r = - 30$ by $- 15$ and simplify.

Divide each term in $- 15 r = - 30$ by $- 15$ .

$\frac{- 15 r}{- 15} = \frac{- 30}{- 15}$

$q = 13 - 9 r$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 r}{- 15} = \frac{- 30}{- 15}$

$q = 13 - 9 r$

Divide $r$ by $1$ .

$r = \frac{- 30}{- 15}$

$q = 13 - 9 r$

$r = \frac{- 30}{- 15}$

$q = 13 - 9 r$

$r = \frac{- 30}{- 15}$

$q = 13 - 9 r$

Simplify the right side.

Divide $- 30$ by $- 15$ .

$r = 2$

$q = 13 - 9 r$

$r = 2$

$q = 13 - 9 r$

$r = 2$

$q = 13 - 9 r$

$r = 2$

$q = 13 - 9 r$

Replace all occurrences of $r$ with $2$ in each equation.

Replace all occurrences of $r$ in $q = 13 - 9 r$ with $2$ .

$q = 13 - 9 \cdot 2$

$r = 2$

Simplify the right side.

Simplify $13 - 9 \cdot 2$ .

Multiply $- 9$ by $2$ .

$q = 13 - 18$

$r = 2$

Subtract $18$ from $13$ .

$q = - 5$

$r = 2$

$q = - 5$

$r = 2$

$q = - 5$

$r = 2$

$q = - 5$

$r = 2$

List all of the solutions.

$q = - 5, r = 2$

Solve the System of Equations 9r+q=13 3r+2q=-4

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