Solve the System of Equations 3s-t-u=5 3s+2t-u=11 6s-3t+2u=-12

$3 s - t - u = 5$ $3 s + 2 t - u = 11$ $6 s - 3 t + 2 u = - 12$

Solve for $s$ in $3 s - t - u = 5$ .

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

Add $t$ to both sides of the equation.

$3 s - u = 5 + t$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

Add $u$ to both sides of the equation.

$3 s = 5 + t + u$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

$3 s = 5 + t + u$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

Divide each term in $3 s = 5 + t + u$ by $3$ and simplify.

Divide each term in $3 s = 5 + t + u$ by $3$ .

$\frac{3 s}{3} = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 s}{3} = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

Divide $s$ by $1$ .

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 s + 2 t - u = 11$

$6 s - 3 t + 2 u = - 12$

Replace all occurrences of $s$ with $\frac{5}{3} + \frac{t}{3} + \frac{u}{3}$ in each equation.

Replace all occurrences of $s$ in $3 s + 2 t - u = 11$ with $\frac{5}{3} + \frac{t}{3} + \frac{u}{3}$ .

$3 (\frac{5}{3} + \frac{t}{3} + \frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Simplify the left side.

Simplify $3 (\frac{5}{3} + \frac{t}{3} + \frac{u}{3}) + 2 t - u$ .

Simplify each term.

Apply the distributive property.

$3 (\frac{5}{3}) + 3 (\frac{t}{3}) + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Simplify.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 (\frac{5}{3}) + 3 (\frac{t}{3}) + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Rewrite the expression.

$5 + 3 (\frac{t}{3}) + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + 3 (\frac{t}{3}) + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Cancel the common factor of $3$ .

Cancel the common factor.

$5 + 3 (\frac{t}{3}) + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Rewrite the expression.

$5 + t + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + t + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Cancel the common factor of $3$ .

Cancel the common factor.

$5 + t + 3 (\frac{u}{3}) + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Rewrite the expression.

$5 + t + u + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + t + u + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + t + u + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + t + u + 2 t - u = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Simplify by adding terms.

Combine the opposite terms in $5 + t + u + 2 t - u$ .

Subtract $u$ from $u$ .

$5 + t + 2 t + 0 = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Add $5 + t + 2 t$ and $0$ .

$5 + t + 2 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + t + 2 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Add $t$ and $2 t$ .

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$6 s - 3 t + 2 u = - 12$

Replace all occurrences of $s$ in $6 s - 3 t + 2 u = - 12$ with $\frac{5}{3} + \frac{t}{3} + \frac{u}{3}$ .

$6 (\frac{5}{3} + \frac{t}{3} + \frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Simplify the left side.

Simplify $6 (\frac{5}{3} + \frac{t}{3} + \frac{u}{3}) - 3 t + 2 u$ .

Simplify each term.

Apply the distributive property.

$6 (\frac{5}{3}) + 6 (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Simplify.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$3 (2) (\frac{5}{3}) + 6 (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Cancel the common factor.

$3 \cdot (2 (\frac{5}{3})) + 6 (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Rewrite the expression.

$2 \cdot 5 + 6 (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$2 \cdot 5 + 6 (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Multiply $2$ by $5$ .

$10 + 6 (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$10 + 3 (2) (\frac{t}{3}) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Cancel the common factor.

$10 + 3 \cdot (2 (\frac{t}{3})) + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Rewrite the expression.

$10 + 2 t + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 + 2 t + 6 (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$10 + 2 t + 3 (2) (\frac{u}{3}) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Cancel the common factor.

$10 + 2 t + 3 \cdot (2 (\frac{u}{3})) - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Rewrite the expression.

$10 + 2 t + 2 u - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 + 2 t + 2 u - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 + 2 t + 2 u - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 + 2 t + 2 u - 3 t + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Simplify by adding terms.

Subtract $3 t$ from $2 t$ .

$10 - t + 2 u + 2 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Add $2 u$ and $2 u$ .

$10 - t + 4 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 - t + 4 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 - t + 4 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 - t + 4 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$10 - t + 4 u = - 12$

$5 + 3 t = 11$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Solve for $t$ in $5 + 3 t = 11$ .

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

Subtract $5$ from both sides of the equation.

$3 t = 11 - 5$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Subtract $5$ from $11$ .

$3 t = 6$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$3 t = 6$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Divide each term in $3 t = 6$ by $3$ and simplify.

Divide each term in $3 t = 6$ by $3$ .

$\frac{3 t}{3} = \frac{6}{3}$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 t}{3} = \frac{6}{3}$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Divide $t$ by $1$ .

$t = \frac{6}{3}$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$t = \frac{6}{3}$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$t = \frac{6}{3}$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$t = 2$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$t = 2$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$t = 2$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$t = 2$

$10 - t + 4 u = - 12$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

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

Replace all occurrences of $t$ in $10 - t + 4 u = - 12$ with $2$ .

$10 - (2) + 4 u = - 12$

$t = 2$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Simplify the left side.

Simplify $10 - (2) + 4 u$ .

Multiply $- 1$ by $2$ .

$10 - 2 + 4 u = - 12$

$t = 2$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Subtract $2$ from $10$ .

$8 + 4 u = - 12$

$t = 2$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$8 + 4 u = - 12$

$t = 2$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

$8 + 4 u = - 12$

$t = 2$

$s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$

Replace all occurrences of $t$ in $s = \frac{5}{3} + \frac{t}{3} + \frac{u}{3}$ with $2$ .

$s = \frac{5}{3} + \frac{2}{3} + \frac{u}{3}$

$8 + 4 u = - 12$

$t = 2$

Simplify the right side.

Simplify $\frac{5}{3} + \frac{2}{3} + \frac{u}{3}$ .

Combine the numerators over the common denominator.

$s = \frac{5 + 2 + u}{3}$

$8 + 4 u = - 12$

$t = 2$

Add $5$ and $2$ .

$s = \frac{7 + u}{3}$

$8 + 4 u = - 12$

$t = 2$

$s = \frac{7 + u}{3}$

$8 + 4 u = - 12$

$t = 2$

$s = \frac{7 + u}{3}$

$8 + 4 u = - 12$

$t = 2$

$s = \frac{7 + u}{3}$

$8 + 4 u = - 12$

$t = 2$

Solve for $u$ in $8 + 4 u = - 12$ .

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

Subtract $8$ from both sides of the equation.

$4 u = - 12 - 8$

$s = \frac{7 + u}{3}$

$t = 2$

Subtract $8$ from $- 12$ .

$4 u = - 20$

$s = \frac{7 + u}{3}$

$t = 2$

$4 u = - 20$

$s = \frac{7 + u}{3}$

$t = 2$

Divide each term in $4 u = - 20$ by $4$ and simplify.

Divide each term in $4 u = - 20$ by $4$ .

$\frac{4 u}{4} = \frac{- 20}{4}$

$s = \frac{7 + u}{3}$

$t = 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 u}{4} = \frac{- 20}{4}$

$s = \frac{7 + u}{3}$

$t = 2$

Divide $u$ by $1$ .

$u = \frac{- 20}{4}$

$s = \frac{7 + u}{3}$

$t = 2$

$u = \frac{- 20}{4}$

$s = \frac{7 + u}{3}$

$t = 2$

$u = \frac{- 20}{4}$

$s = \frac{7 + u}{3}$

$t = 2$

Simplify the right side.

Divide $- 20$ by $4$ .

$u = - 5$

$s = \frac{7 + u}{3}$

$t = 2$

$u = - 5$

$s = \frac{7 + u}{3}$

$t = 2$

$u = - 5$

$s = \frac{7 + u}{3}$

$t = 2$

$u = - 5$

$s = \frac{7 + u}{3}$

$t = 2$

Replace all occurrences of $u$ with $- 5$ in each equation.

Replace all occurrences of $u$ in $s = \frac{7 + u}{3}$ with $- 5$ .

$s = \frac{7 - 5}{3}$

$u = - 5$

$t = 2$

Simplify $s = \frac{7 - 5}{3}$ .

Simplify the left side.

Remove parentheses.

$s = \frac{7 - 5}{3}$

$u = - 5$

$t = 2$

$s = \frac{7 - 5}{3}$

$u = - 5$

$t = 2$

Simplify the right side.

Subtract $5$ from $7$ .

$s = \frac{2}{3}$

$u = - 5$

$t = 2$

$s = \frac{2}{3}$

$u = - 5$

$t = 2$

$s = \frac{2}{3}$

$u = - 5$

$t = 2$

$s = \frac{2}{3}$

$u = - 5$

$t = 2$

List all of the solutions.

$s = \frac{2}{3}, u = - 5, t = 2$

Solve the System of Equations 3s-t-u=5 3s+2t-u=11 6s-3t+2u=-12

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