Finite Math Examples

$- 5 r + 2 s + 4 t = 8$ , $4 r + t = 3$ , $t = 3 r - 3 s - 3$

Step 1

Replace all occurrences of $t$ with $3 r - 3 s - 3$ in each equation.

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Step 1.1

Replace all occurrences of $t$ in $- 5 r + 2 s + 4 t = 8$ with $3 r - 3 s - 3$ .

$- 5 r + 2 s + 4 (3 r - 3 s - 3) = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$- 5 r + 2 s + 4 (3 r) + 4 (- 3 s) + 4 \cdot - 3 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.2.1.1.2

Simplify.

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Step 1.2.1.1.2.1

Multiply $3$ by $4$ .

$- 5 r + 2 s + 12 r + 4 (- 3 s) + 4 \cdot - 3 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.2.1.1.2.2

Multiply $- 3$ by $4$ .

$- 5 r + 2 s + 12 r - 12 s + 4 \cdot - 3 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.2.1.1.2.3

Multiply $4$ by $- 3$ .

$- 5 r + 2 s + 12 r - 12 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

$- 5 r + 2 s + 12 r - 12 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

$- 5 r + 2 s + 12 r - 12 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.2.1.2

Simplify by adding terms.

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Step 1.2.1.2.1

Add $- 5 r$ and $12 r$ .

$7 r + 2 s - 12 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.2.1.2.2

Subtract $12 s$ from $2 s$ .

$7 r - 10 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

$7 r - 10 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

$7 r - 10 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

$7 r - 10 s - 12 = 8$

$4 r + t = 3$

$t = 3 r - 3 s - 3$

Step 1.3

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

$4 r + 3 r - 3 s - 3 = 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 1.4

Simplify the left side.

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Step 1.4.1

Simplify $4 r + 3 r - 3 s - 3$ .

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Step 1.4.1.1

Remove parentheses.

$4 r + 3 r - 3 s - 3 = 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 1.4.1.2

Add $4 r$ and $3 r$ .

$7 r - 3 s - 3 = 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$7 r - 3 s - 3 = 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$7 r - 3 s - 3 = 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$7 r - 3 s - 3 = 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 2

Solve for $r$ in $7 r - 3 s - 3 = 3$ .

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Step 2.1

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

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Step 2.1.1

Add $3 s$ to both sides of the equation.

$7 r - 3 = 3 + 3 s$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 2.1.2

Add $3$ to both sides of the equation.

$7 r = 3 + 3 s + 3$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 2.1.3

Add $3$ and $3$ .

$7 r = 3 s + 6$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$7 r = 3 s + 6$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 2.2

Divide each term in $7 r = 3 s + 6$ by $7$ and simplify.

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Step 2.2.1

Divide each term in $7 r = 3 s + 6$ by $7$ .

$\frac{7 r}{7} = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{7 r}{7} = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 2.2.2.1.2

Divide $r$ by $1$ .

$r = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$r = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$r = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$r = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

$r = \frac{3 s}{7} + \frac{6}{7}$

$7 r - 10 s - 12 = 8$

$t = 3 r - 3 s - 3$

Step 3

Replace all occurrences of $r$ with $\frac{3 s}{7} + \frac{6}{7}$ in each equation.

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Step 3.1

Replace all occurrences of $r$ in $7 r - 10 s - 12 = 8$ with $\frac{3 s}{7} + \frac{6}{7}$ .

$7 (\frac{3 s}{7} + \frac{6}{7}) - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify $7 (\frac{3 s}{7} + \frac{6}{7}) - 10 s - 12$ .

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Step 3.2.1.1

Simplify each term.

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Step 3.2.1.1.1

Apply the distributive property.

$7 (\frac{3 s}{7}) + 7 (\frac{6}{7}) - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2.1.1.2

Cancel the common factor of $7$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$7 (\frac{3 s}{7}) + 7 (\frac{6}{7}) - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2.1.1.2.2

Rewrite the expression.

$3 s + 7 (\frac{6}{7}) - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

$3 s + 7 (\frac{6}{7}) - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2.1.1.3

Cancel the common factor of $7$ .

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Step 3.2.1.1.3.1

Cancel the common factor.

$3 s + 7 (\frac{6}{7}) - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2.1.1.3.2

Rewrite the expression.

$3 s + 6 - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

$3 s + 6 - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

$3 s + 6 - 10 s - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2.1.2

Simplify by adding terms.

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Step 3.2.1.2.1

Subtract $10 s$ from $3 s$ .

$- 7 s + 6 - 12 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.2.1.2.2

Subtract $12$ from $6$ .

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3 r - 3 s - 3$

Step 3.3

Replace all occurrences of $r$ in $t = 3 r - 3 s - 3$ with $\frac{3 s}{7} + \frac{6}{7}$ .

$t = 3 (\frac{3 s}{7} + \frac{6}{7}) - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4

Simplify the right side.

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Step 3.4.1

Simplify $3 (\frac{3 s}{7} + \frac{6}{7}) - 3 s - 3$ .

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Step 3.4.1.1

Simplify each term.

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Step 3.4.1.1.1

Apply the distributive property.

$t = 3 (\frac{3 s}{7}) + 3 (\frac{6}{7}) - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.1.2

Multiply $3 \frac{3 s}{7}$ .

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Step 3.4.1.1.2.1

Combine $3$ and $\frac{3 s}{7}$ .

$t = \frac{3 (3 s)}{7} + 3 (\frac{6}{7}) - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.1.2.2

Multiply $3$ by $3$ .

$t = \frac{9 s}{7} + 3 (\frac{6}{7}) - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = \frac{9 s}{7} + 3 (\frac{6}{7}) - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.1.3

Multiply $3 (\frac{6}{7})$ .

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Step 3.4.1.1.3.1

Combine $3$ and $\frac{6}{7}$ .

$t = \frac{9 s}{7} + \frac{3 \cdot 6}{7} - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.1.3.2

Multiply $3$ by $6$ .

$t = \frac{9 s}{7} + \frac{18}{7} - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = \frac{9 s}{7} + \frac{18}{7} - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = \frac{9 s}{7} + \frac{18}{7} - 3 s - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.2

To write $- 3 s$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$t = \frac{9 s}{7} - 3 s \cdot \frac{7}{7} + \frac{18}{7} - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.3

Combine $- 3 s$ and $\frac{7}{7}$ .

$t = \frac{9 s}{7} + \frac{- 3 s \cdot 7}{7} + \frac{18}{7} - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.4

Combine the numerators over the common denominator.

$t = \frac{9 s - 3 s \cdot 7}{7} + \frac{18}{7} - 3$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.5

Combine the numerators over the common denominator.

$t = - 3 + \frac{9 s - 3 s \cdot 7 + 18}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.6

Multiply $7$ by $- 3$ .

$t = - 3 + \frac{9 s - 21 s + 18}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.7

Subtract $21 s$ from $9 s$ .

$t = - 3 + \frac{- 12 s + 18}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.8

Factor $6$ out of $- 12 s + 18$ .

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Step 3.4.1.8.1

Factor $6$ out of $- 12 s$ .

$t = - 3 + \frac{6 (- 2 s) + 18}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.8.2

Factor $6$ out of $18$ .

$t = - 3 + \frac{6 (- 2 s) + 6 (3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.8.3

Factor $6$ out of $6 (- 2 s) + 6 (3)$ .

$t = - 3 + \frac{6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - 3 + \frac{6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.9

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$t = - 3 \cdot \frac{7}{7} + \frac{6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.10

Simplify terms.

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Step 3.4.1.10.1

Combine $- 3$ and $\frac{7}{7}$ .

$t = \frac{- 3 \cdot 7}{7} + \frac{6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.10.2

Combine the numerators over the common denominator.

$t = \frac{- 3 \cdot 7 + 6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = \frac{- 3 \cdot 7 + 6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11

Simplify the numerator.

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Step 3.4.1.11.1

Factor $3$ out of $- 3 \cdot 7 + 6 (- 2 s + 3)$ .

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Step 3.4.1.11.1.1

Factor $3$ out of $- 3 \cdot 7$ .

$t = \frac{3 (- 1 \cdot 7) + 6 (- 2 s + 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.1.2

Factor $3$ out of $6 (- 2 s + 3)$ .

$t = \frac{3 (- 1 \cdot 7) + 3 (2 (- 2 s + 3))}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.1.3

Factor $3$ out of $3 (- 1 \cdot 7) + 3 (2 (- 2 s + 3))$ .

$t = \frac{3 (- 1 \cdot 7 + 2 (- 2 s + 3))}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = \frac{3 (- 1 \cdot 7 + 2 (- 2 s + 3))}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.2

Multiply $- 1$ by $7$ .

$t = \frac{3 (- 7 + 2 (- 2 s + 3))}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.3

Apply the distributive property.

$t = \frac{3 (- 7 + 2 (- 2 s) + 2 \cdot 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.4

Multiply $- 2$ by $2$ .

$t = \frac{3 (- 7 - 4 s + 2 \cdot 3)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.5

Multiply $2$ by $3$ .

$t = \frac{3 (- 7 - 4 s + 6)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.11.6

Add $- 7$ and $6$ .

$t = \frac{3 (- 4 s - 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = \frac{3 (- 4 s - 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.12

Simplify with factoring out.

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Step 3.4.1.12.1

Factor $- 1$ out of $- 4 s$ .

$t = \frac{3 (- (4 s) - 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.12.2

Rewrite $- 1$ as $- 1 (1)$ .

$t = \frac{3 (- (4 s) - 1 \cdot 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.12.3

Factor $- 1$ out of $- (4 s) - 1 (1)$ .

$t = \frac{3 (- (4 s + 1))}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.12.4

Simplify the expression.

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Step 3.4.1.12.4.1

Rewrite $- (4 s + 1)$ as $- 1 (4 s + 1)$ .

$t = \frac{3 (- 1 (4 s + 1))}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 3.4.1.12.4.2

Move the negative in front of the fraction.

$t = - \frac{3 (4 s + 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - \frac{3 (4 s + 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - \frac{3 (4 s + 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - \frac{3 (4 s + 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - \frac{3 (4 s + 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - \frac{3 (4 s + 1)}{7}$

$- 7 s - 6 = 8$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 4

Solve for $s$ in $- 7 s - 6 = 8$ .

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Step 4.1

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

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Step 4.1.1

Add $6$ to both sides of the equation.

$- 7 s = 8 + 6$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 4.1.2

Add $8$ and $6$ .

$- 7 s = 14$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

$- 7 s = 14$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 4.2

Divide each term in $- 7 s = 14$ by $- 7$ and simplify.

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Step 4.2.1

Divide each term in $- 7 s = 14$ by $- 7$ .

$\frac{- 7 s}{- 7} = \frac{14}{- 7}$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 7 s}{- 7} = \frac{14}{- 7}$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 4.2.2.1.2

Divide $s$ by $1$ .

$s = \frac{14}{- 7}$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

$s = \frac{14}{- 7}$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

$s = \frac{14}{- 7}$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $14$ by $- 7$ .

$s = - 2$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

$s = - 2$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

$s = - 2$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

$s = - 2$

$t = - \frac{3 (4 s + 1)}{7}$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5

Replace all occurrences of $s$ with $- 2$ in each equation.

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Step 5.1

Replace all occurrences of $s$ in $t = - \frac{3 (4 s + 1)}{7}$ with $- 2$ .

$t = - \frac{3 (4 (- 2) + 1)}{7}$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{3 (4 (- 2) + 1)}{7}$ .

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Step 5.2.1.1

Simplify the numerator.

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Step 5.2.1.1.1

Multiply $4$ by $- 2$ .

$t = - \frac{3 (- 8 + 1)}{7}$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5.2.1.1.2

Add $- 8$ and $1$ .

$t = - \frac{3 \cdot - 7}{7}$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = - \frac{3 \cdot - 7}{7}$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5.2.1.2

Simplify the expression.

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Step 5.2.1.2.1

Multiply $3$ by $- 7$ .

$t = - \frac{- 21}{7}$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5.2.1.2.2

Divide $- 21$ by $7$ .

$t = 3$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5.2.1.2.3

Multiply $- 1$ by $- 3$ .

$t = 3$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

$t = 3$

$s = - 2$

$r = \frac{3 s}{7} + \frac{6}{7}$

Step 5.3

Replace all occurrences of $s$ in $r = \frac{3 s}{7} + \frac{6}{7}$ with $- 2$ .

$r = \frac{3 (- 2)}{7} + \frac{6}{7}$

$t = 3$

$s = - 2$

Step 5.4

Simplify the right side.

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Step 5.4.1

Simplify $\frac{3 (- 2)}{7} + \frac{6}{7}$ .

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Step 5.4.1.1

Combine the numerators over the common denominator.

$r = \frac{3 (- 2) + 6}{7}$

$t = 3$

$s = - 2$

Step 5.4.1.2

Simplify the expression.

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Step 5.4.1.2.1

Multiply $3$ by $- 2$ .

$r = \frac{- 6 + 6}{7}$

$t = 3$

$s = - 2$

Step 5.4.1.2.2

Add $- 6$ and $6$ .

$r = \frac{0}{7}$

$t = 3$

$s = - 2$

Step 5.4.1.2.3

Divide $0$ by $7$ .

$r = 0$

$t = 3$

$s = - 2$

$r = 0$

$t = 3$

$s = - 2$

$r = 0$

$t = 3$

$s = - 2$

$r = 0$

$t = 3$

$s = - 2$

$r = 0$

$t = 3$

$s = - 2$

Step 6

List all of the solutions.

$r = 0, t = 3, s = - 2$