Finite Math Examples

$2 x - 3 y - 2 z = 6$ , $x + 2 y + 3 z = 8$ , $3 x - y - 2 z = 5$

Step 1

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

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Step 1.1

Subtract $2 y$ from both sides of the equation.

$x + 3 z = 8 - 2 y$

$2 x - 3 y - 2 z = 6$

$3 x - y - 2 z = 5$

Step 1.2

Subtract $3 z$ from both sides of the equation.

$x = 8 - 2 y - 3 z$

$2 x - 3 y - 2 z = 6$

$3 x - y - 2 z = 5$

$x = 8 - 2 y - 3 z$

$2 x - 3 y - 2 z = 6$

$3 x - y - 2 z = 5$

Step 2

Replace all occurrences of $x$ with $8 - 2 y - 3 z$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2 x - 3 y - 2 z = 6$ with $8 - 2 y - 3 z$ .

$2 (8 - 2 y - 3 z) - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (8 - 2 y - 3 z) - 3 y - 2 z$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$2 \cdot 8 + 2 (- 2 y) + 2 (- 3 z) - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $2$ by $8$ .

$16 + 2 (- 2 y) + 2 (- 3 z) - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.2.1.1.2.2

Multiply $- 2$ by $2$ .

$16 - 4 y + 2 (- 3 z) - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.2.1.1.2.3

Multiply $- 3$ by $2$ .

$16 - 4 y - 6 z - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

$16 - 4 y - 6 z - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

$16 - 4 y - 6 z - 3 y - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $3 y$ from $- 4 y$ .

$16 - 7 y - 6 z - 2 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.2.1.2.2

Subtract $2 z$ from $- 6 z$ .

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$3 x - y - 2 z = 5$

Step 2.3

Replace all occurrences of $x$ in $3 x - y - 2 z = 5$ with $8 - 2 y - 3 z$ .

$3 (8 - 2 y - 3 z) - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $3 (8 - 2 y - 3 z) - y - 2 z$ .

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Step 2.4.1.1

Simplify each term.

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Step 2.4.1.1.1

Apply the distributive property.

$3 \cdot 8 + 3 (- 2 y) + 3 (- 3 z) - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $3$ by $8$ .

$24 + 3 (- 2 y) + 3 (- 3 z) - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 2.4.1.1.2.2

Multiply $- 2$ by $3$ .

$24 - 6 y + 3 (- 3 z) - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 2.4.1.1.2.3

Multiply $- 3$ by $3$ .

$24 - 6 y - 9 z - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$24 - 6 y - 9 z - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$24 - 6 y - 9 z - y - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Subtract $y$ from $- 6 y$ .

$24 - 7 y - 9 z - 2 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 2.4.1.2.2

Subtract $2 z$ from $- 9 z$ .

$24 - 7 y - 11 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$24 - 7 y - 11 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$24 - 7 y - 11 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$24 - 7 y - 11 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$24 - 7 y - 11 z = 5$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3

Solve for $y$ in $24 - 7 y - 11 z = 5$ .

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Step 3.1

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

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Step 3.1.1

Subtract $24$ from both sides of the equation.

$- 7 y - 11 z = 5 - 24$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.1.2

Add $11 z$ to both sides of the equation.

$- 7 y = 5 - 24 + 11 z$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.1.3

Subtract $24$ from $5$ .

$- 7 y = - 19 + 11 z$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$- 7 y = - 19 + 11 z$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.2

Divide each term in $- 7 y = - 19 + 11 z$ by $- 7$ and simplify.

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Step 3.2.1

Divide each term in $- 7 y = - 19 + 11 z$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 19}{- 7} + \frac{11 z}{- 7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 7$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 19}{- 7} + \frac{11 z}{- 7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 19}{- 7} + \frac{11 z}{- 7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$y = \frac{- 19}{- 7} + \frac{11 z}{- 7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$y = \frac{- 19}{- 7} + \frac{11 z}{- 7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Simplify each term.

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Step 3.2.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{19}{7} + \frac{11 z}{- 7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$y = \frac{19}{7} - \frac{11 z}{7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$y = \frac{19}{7} - \frac{11 z}{7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$y = \frac{19}{7} - \frac{11 z}{7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$y = \frac{19}{7} - \frac{11 z}{7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

$y = \frac{19}{7} - \frac{11 z}{7}$

$16 - 7 y - 8 z = 6$

$x = 8 - 2 y - 3 z$

Step 4

Replace all occurrences of $y$ with $\frac{19}{7} - \frac{11 z}{7}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $16 - 7 y - 8 z = 6$ with $\frac{19}{7} - \frac{11 z}{7}$ .

$16 - 7 (\frac{19}{7} - \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $16 - 7 (\frac{19}{7} - \frac{11 z}{7}) - 8 z$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Apply the distributive property.

$16 - 7 (\frac{19}{7}) - 7 (- \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.2

Cancel the common factor of $7$ .

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Step 4.2.1.1.2.1

Factor $7$ out of $- 7$ .

$16 + 7 (- 1) (\frac{19}{7}) - 7 (- \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.2.2

Cancel the common factor.

$16 + 7 \cdot (- 1 (\frac{19}{7})) - 7 (- \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.2.3

Rewrite the expression.

$16 - 1 \cdot 19 - 7 (- \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

$16 - 1 \cdot 19 - 7 (- \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.3

Multiply $- 1$ by $19$ .

$16 - 19 - 7 (- \frac{11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.4

Cancel the common factor of $7$ .

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Step 4.2.1.1.4.1

Move the leading negative in $- \frac{11 z}{7}$ into the numerator.

$16 - 19 - 7 \frac{- 11 z}{7} - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.4.2

Factor $7$ out of $- 7$ .

$16 - 19 + 7 (- 1) (\frac{- 11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.4.3

Cancel the common factor.

$16 - 19 + 7 \cdot (- 1 \frac{- 11 z}{7}) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.4.4

Rewrite the expression.

$16 - 19 - 1 (- 11 z) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

$16 - 19 - 1 (- 11 z) - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.1.5

Multiply $- 11$ by $- 1$ .

$16 - 19 + 11 z - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

$16 - 19 + 11 z - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.2

Simplify by adding terms.

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Step 4.2.1.2.1

Subtract $19$ from $16$ .

$- 3 + 11 z - 8 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.2.1.2.2

Subtract $8 z$ from $11 z$ .

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - 2 y - 3 z$

Step 4.3

Replace all occurrences of $y$ in $x = 8 - 2 y - 3 z$ with $\frac{19}{7} - \frac{11 z}{7}$ .

$x = 8 - 2 (\frac{19}{7} - \frac{11 z}{7}) - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $8 - 2 (\frac{19}{7} - \frac{11 z}{7}) - 3 z$ .

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Step 4.4.1.1

Simplify each term.

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Step 4.4.1.1.1

Apply the distributive property.

$x = 8 - 2 (\frac{19}{7}) - 2 (- \frac{11 z}{7}) - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.1.2

Multiply $- 2 (\frac{19}{7})$ .

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Step 4.4.1.1.2.1

Combine $- 2$ and $\frac{19}{7}$ .

$x = 8 + \frac{- 2 \cdot 19}{7} - 2 (- \frac{11 z}{7}) - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.1.2.2

Multiply $- 2$ by $19$ .

$x = 8 + \frac{- 38}{7} - 2 (- \frac{11 z}{7}) - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 + \frac{- 38}{7} - 2 (- \frac{11 z}{7}) - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.1.3

Multiply $- 2 (- \frac{11 z}{7})$ .

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 2$ .

$x = 8 + \frac{- 38}{7} + 2 (\frac{11 z}{7}) - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.1.3.2

Combine $2$ and $\frac{11 z}{7}$ .

$x = 8 + \frac{- 38}{7} + \frac{2 (11 z)}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.1.3.3

Multiply $11$ by $2$ .

$x = 8 + \frac{- 38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 + \frac{- 38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$x = 8 - \frac{38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 8 - \frac{38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = 8 \cdot \frac{7}{7} - \frac{38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.3

Combine $8$ and $\frac{7}{7}$ .

$x = \frac{8 \cdot 7}{7} - \frac{38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$x = \frac{8 \cdot 7 - 38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $8$ by $7$ .

$x = \frac{56 - 38}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.5.2

Subtract $38$ from $56$ .

$x = \frac{18}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = \frac{18}{7} + \frac{22 z}{7} - 3 z$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.6

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

$x = \frac{18}{7} + \frac{22 z}{7} - 3 z \cdot \frac{7}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.7

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

$x = \frac{18}{7} + \frac{22 z}{7} + \frac{- 3 z \cdot 7}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.8

Combine the numerators over the common denominator.

$x = \frac{18}{7} + \frac{22 z - 3 z \cdot 7}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$x = \frac{18 + 22 z - 3 z \cdot 7}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.10

Multiply $7$ by $- 3$ .

$x = \frac{18 + 22 z - 21 z}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 4.4.1.11

Subtract $21 z$ from $22 z$ .

$x = \frac{18 + z}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = \frac{18 + z}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = \frac{18 + z}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = \frac{18 + z}{7}$

$- 3 + 3 z = 6$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 5

Solve for $z$ in $- 3 + 3 z = 6$ .

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Step 5.1

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

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Step 5.1.1

Add $3$ to both sides of the equation.

$3 z = 6 + 3$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 5.1.2

Add $6$ and $3$ .

$3 z = 9$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

$3 z = 9$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 5.2

Divide each term in $3 z = 9$ by $3$ and simplify.

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Step 5.2.1

Divide each term in $3 z = 9$ by $3$ .

$\frac{3 z}{3} = \frac{9}{3}$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $3$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{3 z}{3} = \frac{9}{3}$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 5.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{9}{3}$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

$z = \frac{9}{3}$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

$z = \frac{9}{3}$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $9$ by $3$ .

$z = 3$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

$z = 3$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

$z = 3$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

$z = 3$

$x = \frac{18 + z}{7}$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 6

Replace all occurrences of $z$ with $3$ in each equation.

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Step 6.1

Replace all occurrences of $z$ in $x = \frac{18 + z}{7}$ with $3$ .

$x = \frac{18 + 3}{7}$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 6.2

Simplify $x = \frac{18 + 3}{7}$ .

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Step 6.2.1

Simplify the left side.

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Step 6.2.1.1

Remove parentheses.

$x = \frac{18 + 3}{7}$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = \frac{18 + 3}{7}$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 6.2.2

Simplify the right side.

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Step 6.2.2.1

Simplify $\frac{18 + 3}{7}$ .

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Step 6.2.2.1.1

Add $18$ and $3$ .

$x = \frac{21}{7}$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 6.2.2.1.2

Divide $21$ by $7$ .

$x = 3$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 3$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 3$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

$x = 3$

$z = 3$

$y = \frac{19}{7} - \frac{11 z}{7}$

Step 6.3

Replace all occurrences of $z$ in $y = \frac{19}{7} - \frac{11 z}{7}$ with $3$ .

$y = \frac{19}{7} - \frac{11 (3)}{7}$

$x = 3$

$z = 3$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{19}{7} - \frac{11 (3)}{7}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$y = \frac{19 - 11 \cdot 3}{7}$

$x = 3$

$z = 3$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $- 11$ by $3$ .

$y = \frac{19 - 33}{7}$

$x = 3$

$z = 3$

Step 6.4.1.2.2

Subtract $33$ from $19$ .

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

$x = 3$

$z = 3$

Step 6.4.1.2.3

Divide $- 14$ by $7$ .

$y = - 2$

$x = 3$

$z = 3$

$y = - 2$

$x = 3$

$z = 3$

$y = - 2$

$x = 3$

$z = 3$

$y = - 2$

$x = 3$

$z = 3$

$y = - 2$

$x = 3$

$z = 3$

Step 7

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(3, - 2, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(3, - 2, 3)$

Equation Form:

$x = 3, y = - 2, z = 3$