Finite Math Examples

$x + 3 y + 5 z = 38$ , $- x + y + 2 z = 3$ , $x + y - 2 z = 7$

Step 1

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

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Step 1.1

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

$x + 5 z = 38 - 3 y$

$- x + y + 2 z = 3$

$x + y - 2 z = 7$

Step 1.2

Subtract $5 z$ from both sides of the equation.

$x = 38 - 3 y - 5 z$

$- x + y + 2 z = 3$

$x + y - 2 z = 7$

$x = 38 - 3 y - 5 z$

$- x + y + 2 z = 3$

$x + y - 2 z = 7$

Step 2

Replace all occurrences of $x$ with $38 - 3 y - 5 z$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- x + y + 2 z = 3$ with $38 - 3 y - 5 z$ .

$- (38 - 3 y - 5 z) + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- (38 - 3 y - 5 z) + y + 2 z$ .

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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.

$- 1 \cdot 38 - (- 3 y) - (- 5 z) + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $- 1$ by $38$ .

$- 38 - (- 3 y) - (- 5 z) + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.2.1.1.2.2

Multiply $- 3$ by $- 1$ .

$- 38 + 3 y - (- 5 z) + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.2.1.1.2.3

Multiply $- 5$ by $- 1$ .

$- 38 + 3 y + 5 z + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

$- 38 + 3 y + 5 z + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

$- 38 + 3 y + 5 z + y + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $3 y$ and $y$ .

$- 38 + 4 y + 5 z + 2 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.2.1.2.2

Add $5 z$ and $2 z$ .

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$x + y - 2 z = 7$

Step 2.3

Replace all occurrences of $x$ in $x + y - 2 z = 7$ with $38 - 3 y - 5 z$ .

$(38 - 3 y - 5 z) + y - 2 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $(38 - 3 y - 5 z) + y - 2 z$ .

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Step 2.4.1.1

Add $- 3 y$ and $y$ .

$38 - 2 y - 5 z - 2 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 2.4.1.2

Subtract $2 z$ from $- 5 z$ .

$38 - 2 y - 7 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$38 - 2 y - 7 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$38 - 2 y - 7 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$38 - 2 y - 7 z = 7$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3

Solve for $y$ in $38 - 2 y - 7 z = 7$ .

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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 $38$ from both sides of the equation.

$- 2 y - 7 z = 7 - 38$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3.1.2

Add $7 z$ to both sides of the equation.

$- 2 y = 7 - 38 + 7 z$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3.1.3

Subtract $38$ from $7$ .

$- 2 y = - 31 + 7 z$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$- 2 y = - 31 + 7 z$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3.2

Divide each term in $- 2 y = - 31 + 7 z$ by $- 2$ and simplify.

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Step 3.2.1

Divide each term in $- 2 y = - 31 + 7 z$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 31}{- 2} + \frac{7 z}{- 2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 31}{- 2} + \frac{7 z}{- 2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 31}{- 2} + \frac{7 z}{- 2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$y = \frac{- 31}{- 2} + \frac{7 z}{- 2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$y = \frac{- 31}{- 2} + \frac{7 z}{- 2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

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.

$y = \frac{31}{2} + \frac{7 z}{- 2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 3.2.3.1.2

Move the negative in front of the fraction.

$y = \frac{31}{2} - \frac{7 z}{2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$y = \frac{31}{2} - \frac{7 z}{2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$y = \frac{31}{2} - \frac{7 z}{2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$y = \frac{31}{2} - \frac{7 z}{2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

$y = \frac{31}{2} - \frac{7 z}{2}$

$- 38 + 4 y + 7 z = 3$

$x = 38 - 3 y - 5 z$

Step 4

Replace all occurrences of $y$ with $\frac{31}{2} - \frac{7 z}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $- 38 + 4 y + 7 z = 3$ with $\frac{31}{2} - \frac{7 z}{2}$ .

$- 38 + 4 (\frac{31}{2} - \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- 38 + 4 (\frac{31}{2} - \frac{7 z}{2}) + 7 z$ .

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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.

$- 38 + 4 (\frac{31}{2}) + 4 (- \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Factor $2$ out of $4$ .

$- 38 + 2 (2) (\frac{31}{2}) + 4 (- \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.2.2

Cancel the common factor.

$- 38 + 2 \cdot (2 (\frac{31}{2})) + 4 (- \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.2.3

Rewrite the expression.

$- 38 + 2 \cdot 31 + 4 (- \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

$- 38 + 2 \cdot 31 + 4 (- \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.3

Multiply $2$ by $31$ .

$- 38 + 62 + 4 (- \frac{7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.4

Cancel the common factor of $2$ .

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Step 4.2.1.1.4.1

Move the leading negative in $- \frac{7 z}{2}$ into the numerator.

$- 38 + 62 + 4 (\frac{- 7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.4.2

Factor $2$ out of $4$ .

$- 38 + 62 + 2 (2) (\frac{- 7 z}{2}) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.4.3

Cancel the common factor.

$- 38 + 62 + 2 \cdot (2 (\frac{- 7 z}{2})) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.4.4

Rewrite the expression.

$- 38 + 62 + 2 (- 7 z) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

$- 38 + 62 + 2 (- 7 z) + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.1.5

Multiply $- 7$ by $2$ .

$- 38 + 62 - 14 z + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

$- 38 + 62 - 14 z + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.2

Simplify by adding terms.

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Step 4.2.1.2.1

Add $- 38$ and $62$ .

$24 - 14 z + 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.2.1.2.2

Add $- 14 z$ and $7 z$ .

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - 3 y - 5 z$

Step 4.3

Replace all occurrences of $y$ in $x = 38 - 3 y - 5 z$ with $\frac{31}{2} - \frac{7 z}{2}$ .

$x = 38 - 3 (\frac{31}{2} - \frac{7 z}{2}) - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $38 - 3 (\frac{31}{2} - \frac{7 z}{2}) - 5 z$ .

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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.

$x = 38 - 3 (\frac{31}{2}) - 3 (- \frac{7 z}{2}) - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.1.2

Multiply $- 3 (\frac{31}{2})$ .

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Step 4.4.1.1.2.1

Combine $- 3$ and $\frac{31}{2}$ .

$x = 38 + \frac{- 3 \cdot 31}{2} - 3 (- \frac{7 z}{2}) - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.1.2.2

Multiply $- 3$ by $31$ .

$x = 38 + \frac{- 93}{2} - 3 (- \frac{7 z}{2}) - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 + \frac{- 93}{2} - 3 (- \frac{7 z}{2}) - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.1.3

Multiply $- 3 (- \frac{7 z}{2})$ .

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 3$ .

$x = 38 + \frac{- 93}{2} + 3 (\frac{7 z}{2}) - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.1.3.2

Combine $3$ and $\frac{7 z}{2}$ .

$x = 38 + \frac{- 93}{2} + \frac{3 (7 z)}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.1.3.3

Multiply $7$ by $3$ .

$x = 38 + \frac{- 93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 + \frac{- 93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.1.4

Move the negative in front of the fraction.

$x = 38 - \frac{93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 38 - \frac{93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.2

To write $38$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = 38 \cdot \frac{2}{2} - \frac{93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.3

Combine $38$ and $\frac{2}{2}$ .

$x = \frac{38 \cdot 2}{2} - \frac{93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$x = \frac{38 \cdot 2 - 93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $38$ by $2$ .

$x = \frac{76 - 93}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.5.2

Subtract $93$ from $76$ .

$x = \frac{- 17}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = \frac{- 17}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.6

Move the negative in front of the fraction.

$x = - \frac{17}{2} + \frac{21 z}{2} - 5 z$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.7

To write $- 5 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{17}{2} + \frac{21 z}{2} - 5 z \cdot \frac{2}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.8

Combine $- 5 z$ and $\frac{2}{2}$ .

$x = - \frac{17}{2} + \frac{21 z}{2} + \frac{- 5 z \cdot 2}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.9

Combine the numerators over the common denominator.

$x = - \frac{17}{2} + \frac{21 z - 5 z \cdot 2}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.10

Combine the numerators over the common denominator.

$x = \frac{- 17 + 21 z - 5 z \cdot 2}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.11

Multiply $2$ by $- 5$ .

$x = \frac{- 17 + 21 z - 10 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.12

Subtract $10 z$ from $21 z$ .

$x = \frac{- 17 + 11 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.13

Rewrite $- 17$ as $- 1 (17)$ .

$x = \frac{- 1 \cdot 17 + 11 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.14

Factor $- 1$ out of $11 z$ .

$x = \frac{- 1 \cdot 17 - (- 11 z)}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.15

Factor $- 1$ out of $- 1 (17) - (- 11 z)$ .

$x = \frac{- 1 (17 - 11 z)}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 4.4.1.16

Move the negative in front of the fraction.

$x = - \frac{17 - 11 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = - \frac{17 - 11 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = - \frac{17 - 11 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = - \frac{17 - 11 z}{2}$

$24 - 7 z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 5

Solve for $z$ in $24 - 7 z = 3$ .

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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

Subtract $24$ from both sides of the equation.

$- 7 z = 3 - 24$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 5.1.2

Subtract $24$ from $3$ .

$- 7 z = - 21$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

$- 7 z = - 21$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 5.2

Divide each term in $- 7 z = - 21$ by $- 7$ and simplify.

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Step 5.2.1

Divide each term in $- 7 z = - 21$ by $- 7$ .

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

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $- 7$ .

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Step 5.2.2.1.1

Cancel the common factor.

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

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 5.2.2.1.2

Divide $z$ by $1$ .

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

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

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

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

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

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 21$ by $- 7$ .

$z = 3$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

$z = 3$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

$z = 3$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

$z = 3$

$x = - \frac{17 - 11 z}{2}$

$y = \frac{31}{2} - \frac{7 z}{2}$

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 $x = - \frac{17 - 11 z}{2}$ with $3$ .

$x = - \frac{17 - 11 \cdot 3}{2}$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{17 - 11 \cdot 3}{2}$ .

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Step 6.2.1.1

Simplify the numerator.

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Step 6.2.1.1.1

Multiply $- 11$ by $3$ .

$x = - \frac{17 - 33}{2}$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 6.2.1.1.2

Subtract $33$ from $17$ .

$x = - \frac{- 16}{2}$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = - \frac{- 16}{2}$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 6.2.1.2

Simplify the expression.

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Step 6.2.1.2.1

Divide $- 16$ by $2$ .

$x = 8$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 6.2.1.2.2

Multiply $- 1$ by $- 8$ .

$x = 8$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 8$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 8$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

$x = 8$

$z = 3$

$y = \frac{31}{2} - \frac{7 z}{2}$

Step 6.3

Replace all occurrences of $z$ in $y = \frac{31}{2} - \frac{7 z}{2}$ with $3$ .

$y = \frac{31}{2} - \frac{7 (3)}{2}$

$x = 8$

$z = 3$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $\frac{31}{2} - \frac{7 (3)}{2}$ .

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Step 6.4.1.1

Combine the numerators over the common denominator.

$y = \frac{31 - 7 \cdot 3}{2}$

$x = 8$

$z = 3$

Step 6.4.1.2

Simplify the expression.

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Step 6.4.1.2.1

Multiply $- 7$ by $3$ .

$y = \frac{31 - 21}{2}$

$x = 8$

$z = 3$

Step 6.4.1.2.2

Subtract $21$ from $31$ .

$y = \frac{10}{2}$

$x = 8$

$z = 3$

Step 6.4.1.2.3

Divide $10$ by $2$ .

$y = 5$

$x = 8$

$z = 3$

$y = 5$

$x = 8$

$z = 3$

$y = 5$

$x = 8$

$z = 3$

$y = 5$

$x = 8$

$z = 3$

$y = 5$

$x = 8$

$z = 3$

Step 7

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

$(8, 5, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(8, 5, 3)$

Equation Form:

$x = 8, y = 5, z = 3$