Solve the System of Equations 4r-4s+4t=-4 4r+s-2t=5 -3r-3s-4t=-16

$4 r - 4 s + 4 t = - 4$ $4 r + s - 2 t = 5$ $- 3 r - 3 s - 4 t = - 16$

Step 1

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

Subtract $4 r$ from both sides of the equation.

$s - 2 t = 5 - 4 r$

$4 r - 4 s + 4 t = - 4$

$- 3 r - 3 s - 4 t = - 16$

Add $2 t$ to both sides of the equation.

$s = 5 - 4 r + 2 t$

$4 r - 4 s + 4 t = - 4$

$- 3 r - 3 s - 4 t = - 16$

$s = 5 - 4 r + 2 t$

$4 r - 4 s + 4 t = - 4$

$- 3 r - 3 s - 4 t = - 16$

Step 2

Replace all occurrences of $s$ with $5 - 4 r + 2 t$ in each equation.

Replace all occurrences of $s$ in $4 r - 4 s + 4 t = - 4$ with $5 - 4 r + 2 t$ .

$4 r - 4 (5 - 4 r + 2 t) + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Simplify the left side.

Simplify $4 r - 4 (5 - 4 r + 2 t) + 4 t$ .

Simplify each term.

Apply the distributive property.

$4 r - 4 \cdot 5 - 4 (- 4 r) - 4 (2 t) + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Simplify.

Multiply $- 4$ by $5$ .

$4 r - 20 - 4 (- 4 r) - 4 (2 t) + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Multiply $- 4$ by $- 4$ .

$4 r - 20 + 16 r - 4 (2 t) + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Multiply $2$ by $- 4$ .

$4 r - 20 + 16 r - 8 t + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

$4 r - 20 + 16 r - 8 t + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

$4 r - 20 + 16 r - 8 t + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Simplify by adding terms.

Add $4 r$ and $16 r$ .

$20 r - 20 - 8 t + 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Add $- 8 t$ and $4 t$ .

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 3 s - 4 t = - 16$

Replace all occurrences of $s$ in $- 3 r - 3 s - 4 t = - 16$ with $5 - 4 r + 2 t$ .

$- 3 r - 3 (5 - 4 r + 2 t) - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Simplify the left side.

Simplify $- 3 r - 3 (5 - 4 r + 2 t) - 4 t$ .

Simplify each term.

Apply the distributive property.

$- 3 r - 3 \cdot 5 - 3 (- 4 r) - 3 (2 t) - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Simplify.

Multiply $- 3$ by $5$ .

$- 3 r - 15 - 3 (- 4 r) - 3 (2 t) - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Multiply $- 4$ by $- 3$ .

$- 3 r - 15 + 12 r - 3 (2 t) - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Multiply $2$ by $- 3$ .

$- 3 r - 15 + 12 r - 6 t - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 15 + 12 r - 6 t - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$- 3 r - 15 + 12 r - 6 t - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Simplify by adding terms.

Add $- 3 r$ and $12 r$ .

$9 r - 15 - 6 t - 4 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Subtract $4 t$ from $- 6 t$ .

$9 r - 15 - 10 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$9 r - 15 - 10 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$9 r - 15 - 10 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$9 r - 15 - 10 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$9 r - 15 - 10 t = - 16$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Step 3

Solve for $r$ in $9 r - 15 - 10 t = - 16$ .

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

Add $15$ to both sides of the equation.

$9 r - 10 t = - 16 + 15$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Add $10 t$ to both sides of the equation.

$9 r = - 16 + 15 + 10 t$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Add $- 16$ and $15$ .

$9 r = - 1 + 10 t$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$9 r = - 1 + 10 t$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Divide each term in $9 r = - 1 + 10 t$ by $9$ and simplify.

Divide each term in $9 r = - 1 + 10 t$ by $9$ .

$\frac{9 r}{9} = \frac{- 1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 r}{9} = \frac{- 1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Divide $r$ by $1$ .

$r = \frac{- 1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$r = \frac{- 1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$r = \frac{- 1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Simplify the right side.

Move the negative in front of the fraction.

$r = - \frac{1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$20 r - 20 - 4 t = - 4$

$s = 5 - 4 r + 2 t$

Step 4

Replace all occurrences of $r$ with $- \frac{1}{9} + \frac{10 t}{9}$ in each equation.

Replace all occurrences of $r$ in $20 r - 20 - 4 t = - 4$ with $- \frac{1}{9} + \frac{10 t}{9}$ .

$20 (- \frac{1}{9} + \frac{10 t}{9}) - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Simplify the left side.

Simplify $20 (- \frac{1}{9} + \frac{10 t}{9}) - 20 - 4 t$ .

Simplify each term.

Apply the distributive property.

$20 (- \frac{1}{9}) + 20 (\frac{10 t}{9}) - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Multiply $20 (- \frac{1}{9})$ .

Multiply $- 1$ by $20$ .

$- 20 (\frac{1}{9}) + 20 (\frac{10 t}{9}) - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Combine $- 20$ and $\frac{1}{9}$ .

$\frac{- 20}{9} + 20 (\frac{10 t}{9}) - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$\frac{- 20}{9} + 20 (\frac{10 t}{9}) - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Multiply $20 \frac{10 t}{9}$ .

Combine $20$ and $\frac{10 t}{9}$ .

$\frac{- 20}{9} + \frac{20 (10 t)}{9} - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Multiply $10$ by $20$ .

$\frac{- 20}{9} + \frac{200 t}{9} - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$\frac{- 20}{9} + \frac{200 t}{9} - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Move the negative in front of the fraction.

$- \frac{20}{9} + \frac{200 t}{9} - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$- \frac{20}{9} + \frac{200 t}{9} - 20 - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{200 t}{9} - \frac{20}{9} - 20 \cdot \frac{9}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Combine $- 20$ and $\frac{9}{9}$ .

$\frac{200 t}{9} - \frac{20}{9} + \frac{- 20 \cdot 9}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Combine the numerators over the common denominator.

$\frac{200 t}{9} + \frac{- 20 - 20 \cdot 9}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Simplify the numerator.

Multiply $- 20$ by $9$ .

$\frac{200 t}{9} + \frac{- 20 - 180}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Subtract $180$ from $- 20$ .

$\frac{200 t}{9} + \frac{- 200}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$\frac{200 t}{9} + \frac{- 200}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Move the negative in front of the fraction.

$\frac{200 t}{9} - \frac{200}{9} - 4 t = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

To write $- 4 t$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{200 t}{9} - 4 t \cdot \frac{9}{9} - \frac{200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Combine $- 4 t$ and $\frac{9}{9}$ .

$\frac{200 t}{9} + \frac{- 4 t \cdot 9}{9} - \frac{200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Combine the numerators over the common denominator.

$\frac{200 t - 4 t \cdot 9}{9} - \frac{200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Combine the numerators over the common denominator.

$\frac{200 t - 4 t \cdot 9 - 200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Multiply $9$ by $- 4$ .

$\frac{200 t - 36 t - 200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Subtract $36 t$ from $200 t$ .

$\frac{164 t - 200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Factor $4$ out of $164 t - 200$ .

Factor $4$ out of $164 t$ .

$\frac{4 (41 t) - 200}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Factor $4$ out of $- 200$ .

$\frac{4 (41 t) + 4 (- 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Factor $4$ out of $4 (41 t) + 4 (- 50)$ .

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 - 4 r + 2 t$

Replace all occurrences of $r$ in $s = 5 - 4 r + 2 t$ with $- \frac{1}{9} + \frac{10 t}{9}$ .

$s = 5 - 4 (- \frac{1}{9} + \frac{10 t}{9}) + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify the right side.

Simplify $5 - 4 (- \frac{1}{9} + \frac{10 t}{9}) + 2 t$ .

Simplify each term.

Apply the distributive property.

$s = 5 - 4 (- \frac{1}{9}) - 4 \frac{10 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Multiply $- 4 (- \frac{1}{9})$ .

Multiply $- 1$ by $- 4$ .

$s = 5 + 4 (\frac{1}{9}) - 4 \frac{10 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Combine $4$ and $\frac{1}{9}$ .

$s = 5 + \frac{4}{9} - 4 \frac{10 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 + \frac{4}{9} - 4 \frac{10 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Multiply $- 4 \frac{10 t}{9}$ .

Combine $- 4$ and $\frac{10 t}{9}$ .

$s = 5 + \frac{4}{9} + \frac{- 4 (10 t)}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Multiply $10$ by $- 4$ .

$s = 5 + \frac{4}{9} + \frac{- 40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 + \frac{4}{9} + \frac{- 40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Move the negative in front of the fraction.

$s = 5 + \frac{4}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 5 + \frac{4}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$s = 5 \cdot \frac{9}{9} + \frac{4}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Combine $5$ and $\frac{9}{9}$ .

$s = \frac{5 \cdot 9}{9} + \frac{4}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Combine the numerators over the common denominator.

$s = \frac{5 \cdot 9 + 4}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify the numerator.

Multiply $5$ by $9$ .

$s = \frac{45 + 4}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Add $45$ and $4$ .

$s = \frac{49}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = \frac{49}{9} - \frac{40 t}{9} + 2 t$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

To write $2 t$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$s = \frac{49}{9} - \frac{40 t}{9} + 2 t \cdot \frac{9}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Combine $2 t$ and $\frac{9}{9}$ .

$s = \frac{49}{9} - \frac{40 t}{9} + \frac{2 t \cdot 9}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Combine the numerators over the common denominator.

$s = \frac{49}{9} + \frac{- 40 t + 2 t \cdot 9}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Combine the numerators over the common denominator.

$s = \frac{49 - 40 t + 2 t \cdot 9}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Multiply $9$ by $2$ .

$s = \frac{49 - 40 t + 18 t}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Add $- 40 t$ and $18 t$ .

$s = \frac{49 - 22 t}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = \frac{49 - 22 t}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = \frac{49 - 22 t}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = \frac{49 - 22 t}{9}$

$\frac{4 (41 t - 50)}{9} = - 4$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Step 5

Solve for $t$ in $\frac{4 (41 t - 50)}{9} = - 4$ .

Multiply both sides by $9$ .

$\frac{4 (41 t - 50)}{9} \cdot 9 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify.

Simplify the left side.

Simplify $\frac{4 (41 t - 50)}{9} \cdot 9$ .

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{4 (41 t - 50)}{9} \cdot 9 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Rewrite the expression.

$4 (41 t - 50) = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$4 (41 t - 50) = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Apply the distributive property.

$4 (41 t) + 4 \cdot - 50 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Multiply.

Multiply $41$ by $4$ .

$164 t + 4 \cdot - 50 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Multiply $4$ by $- 50$ .

$164 t - 200 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$164 t - 200 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$164 t - 200 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$164 t - 200 = - 4 \cdot 9$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify the right side.

Multiply $- 4$ by $9$ .

$164 t - 200 = - 36$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$164 t - 200 = - 36$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$164 t - 200 = - 36$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Solve for $t$ .

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

Add $200$ to both sides of the equation.

$164 t = - 36 + 200$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Add $- 36$ and $200$ .

$164 t = 164$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$164 t = 164$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Divide each term in $164 t = 164$ by $164$ and simplify.

Divide each term in $164 t = 164$ by $164$ .

$\frac{164 t}{164} = \frac{164}{164}$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify the left side.

Cancel the common factor of $164$ .

Cancel the common factor.

$\frac{164 t}{164} = \frac{164}{164}$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Divide $t$ by $1$ .

$t = \frac{164}{164}$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$t = \frac{164}{164}$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$t = \frac{164}{164}$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify the right side.

Divide $164$ by $164$ .

$t = 1$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$t = 1$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$t = 1$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$t = 1$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$t = 1$

$s = \frac{49 - 22 t}{9}$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Step 6

Replace all occurrences of $t$ with $1$ in each equation.

Replace all occurrences of $t$ in $s = \frac{49 - 22 t}{9}$ with $1$ .

$s = \frac{49 - 22 \cdot 1}{9}$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Simplify the right side.

Simplify $\frac{49 - 22 \cdot 1}{9}$ .

Simplify the numerator.

Multiply $- 22$ by $1$ .

$s = \frac{49 - 22}{9}$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Subtract $22$ from $49$ .

$s = \frac{27}{9}$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = \frac{27}{9}$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Divide $27$ by $9$ .

$s = 3$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 3$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

$s = 3$

$t = 1$

$r = - \frac{1}{9} + \frac{10 t}{9}$

Replace all occurrences of $t$ in $r = - \frac{1}{9} + \frac{10 t}{9}$ with $1$ .

$r = - \frac{1}{9} + \frac{10 (1)}{9}$

$s = 3$

$t = 1$

Simplify the right side.

Simplify $- \frac{1}{9} + \frac{10 (1)}{9}$ .

Combine the numerators over the common denominator.

$r = \frac{- 1 + 10 (1)}{9}$

$s = 3$

$t = 1$

Simplify the expression.

Multiply $10$ by $1$ .

$r = \frac{- 1 + 10}{9}$

$s = 3$

$t = 1$

Add $- 1$ and $10$ .

$r = \frac{9}{9}$

$s = 3$

$t = 1$

Divide $9$ by $9$ .

$r = 1$

$s = 3$

$t = 1$

$r = 1$

$s = 3$

$t = 1$

$r = 1$

$s = 3$

$t = 1$

$r = 1$

$s = 3$

$t = 1$

$r = 1$

$s = 3$

$t = 1$

Step 7

List all of the solutions.

$r = 1, s = 3, t = 1$

Solve the System of Equations 4r-4s+4t=-4 4r+s-2t=5 -3r-3s-4t=-16

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