Algebra Examples

$2 x + 3 y + 7 z = 13$ , $3 x + 2 y - 5 z = - 22$ , $5 x + 7 y - 3 z = - 28$

Step 1

Solve for $x$ in $2 x + 3 y + 7 z = 13$ .

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Step 1.1

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

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Step 1.1.1

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

$2 x + 7 z = 13 - 3 y$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 1.1.2

Subtract $7 z$ from both sides of the equation.

$2 x = 13 - 3 y - 7 z$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$2 x = 13 - 3 y - 7 z$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 1.2

Divide each term in $2 x = 13 - 3 y - 7 z$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 x = 13 - 3 y - 7 z$ by $2$ .

$\frac{2 x}{2} = \frac{13}{2} + \frac{- 3 y}{2} + \frac{- 7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{13}{2} + \frac{- 3 y}{2} + \frac{- 7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{13}{2} + \frac{- 3 y}{2} + \frac{- 7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$x = \frac{13}{2} + \frac{- 3 y}{2} + \frac{- 7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$x = \frac{13}{2} + \frac{- 3 y}{2} + \frac{- 7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$x = \frac{13}{2} - \frac{3 y}{2} + \frac{- 7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$3 x + 2 y - 5 z = - 22$

$5 x + 7 y - 3 z = - 28$

Step 2

Replace all occurrences of $x$ with $\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x + 2 y - 5 z = - 22$ with $\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$ .

$3 (\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}) + 2 y - 5 z$ .

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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.

$3 (\frac{13}{2}) + 3 (- \frac{3 y}{2}) + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $3 (\frac{13}{2})$ .

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Step 2.2.1.1.2.1.1

Combine $3$ and $\frac{13}{2}$ .

$\frac{3 \cdot 13}{2} + 3 (- \frac{3 y}{2}) + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.1.2

Multiply $3$ by $13$ .

$\frac{39}{2} + 3 (- \frac{3 y}{2}) + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{39}{2} + 3 (- \frac{3 y}{2}) + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.2

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

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Step 2.2.1.1.2.2.1

Multiply $- 1$ by $3$ .

$\frac{39}{2} - 3 \frac{3 y}{2} + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.2.2

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

$\frac{39}{2} + \frac{- 3 (3 y)}{2} + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.2.3

Multiply $3$ by $- 3$ .

$\frac{39}{2} + \frac{- 9 y}{2} + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{39}{2} + \frac{- 9 y}{2} + 3 (- \frac{7 z}{2}) + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.3

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

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Step 2.2.1.1.2.3.1

Multiply $- 1$ by $3$ .

$\frac{39}{2} + \frac{- 9 y}{2} - 3 \frac{7 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.3.2

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

$\frac{39}{2} + \frac{- 9 y}{2} + \frac{- 3 (7 z)}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.2.3.3

Multiply $7$ by $- 3$ .

$\frac{39}{2} + \frac{- 9 y}{2} + \frac{- 21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{39}{2} + \frac{- 9 y}{2} + \frac{- 21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{39}{2} + \frac{- 9 y}{2} + \frac{- 21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.3

Simplify each term.

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Step 2.2.1.1.3.1

Move the negative in front of the fraction.

$\frac{39}{2} - \frac{9 y}{2} + \frac{- 21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.1.3.2

Move the negative in front of the fraction.

$\frac{39}{2} - \frac{9 y}{2} - \frac{21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{39}{2} - \frac{9 y}{2} - \frac{21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{39}{2} - \frac{9 y}{2} - \frac{21 z}{2} + 2 y - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.2

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

$\frac{39}{2} - \frac{21 z}{2} - \frac{9 y}{2} + 2 y \cdot \frac{2}{2} - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.3

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

$\frac{39}{2} - \frac{21 z}{2} - \frac{9 y}{2} + \frac{2 y \cdot 2}{2} - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.4

Combine the numerators over the common denominator.

$\frac{39}{2} - \frac{21 z}{2} + \frac{- 9 y + 2 y \cdot 2}{2} - 5 z = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.5

Combine the numerators over the common denominator.

$- 5 z + \frac{39 - 21 z - 9 y + 2 y \cdot 2}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.6

Multiply $2$ by $2$ .

$- 5 z + \frac{39 - 21 z - 9 y + 4 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.7

Add $- 9 y$ and $4 y$ .

$- 5 z + \frac{39 - 21 z - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.8

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

$- 5 z \cdot \frac{2}{2} + \frac{39 - 21 z - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.9

Simplify terms.

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Step 2.2.1.9.1

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

$\frac{- 5 z \cdot 2}{2} + \frac{39 - 21 z - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.9.2

Combine the numerators over the common denominator.

$\frac{- 5 z \cdot 2 + 39 - 21 z - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{- 5 z \cdot 2 + 39 - 21 z - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.10

Simplify the numerator.

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Step 2.2.1.10.1

Multiply $2$ by $- 5$ .

$\frac{- 10 z + 39 - 21 z - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.10.2

Subtract $21 z$ from $- 10 z$ .

$\frac{- 31 z + 39 - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$\frac{- 31 z + 39 - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11

Simplify with factoring out.

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Step 2.2.1.11.1

Factor $- 1$ out of $- 31 z$ .

$\frac{- (31 z) + 39 - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11.2

Rewrite $39$ as $- 1 (- 39)$ .

$\frac{- (31 z) - 1 \cdot - 39 - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11.3

Factor $- 1$ out of $- (31 z) - 1 (- 39)$ .

$\frac{- (31 z - 39) - 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11.4

Factor $- 1$ out of $- 5 y$ .

$\frac{- (31 z - 39) - (5 y)}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11.5

Factor $- 1$ out of $- (31 z - 39) - (5 y)$ .

$\frac{- (31 z - 39 + 5 y)}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11.6

Simplify the expression.

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Step 2.2.1.11.6.1

Rewrite $- (31 z - 39 + 5 y)$ as $- 1 (31 z - 39 + 5 y)$ .

$\frac{- 1 (31 z - 39 + 5 y)}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.2.1.11.6.2

Move the negative in front of the fraction.

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$5 x + 7 y - 3 z = - 28$

Step 2.3

Replace all occurrences of $x$ in $5 x + 7 y - 3 z = - 28$ with $\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$ .

$5 (\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $5 (\frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}) + 7 y - 3 z$ .

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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.

$5 (\frac{13}{2}) + 5 (- \frac{3 y}{2}) + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $5 (\frac{13}{2})$ .

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Step 2.4.1.1.2.1.1

Combine $5$ and $\frac{13}{2}$ .

$\frac{5 \cdot 13}{2} + 5 (- \frac{3 y}{2}) + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.1.2

Multiply $5$ by $13$ .

$\frac{65}{2} + 5 (- \frac{3 y}{2}) + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{65}{2} + 5 (- \frac{3 y}{2}) + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.2

Multiply $5 (- \frac{3 y}{2})$ .

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Step 2.4.1.1.2.2.1

Multiply $- 1$ by $5$ .

$\frac{65}{2} - 5 \frac{3 y}{2} + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.2.2

Combine $- 5$ and $\frac{3 y}{2}$ .

$\frac{65}{2} + \frac{- 5 (3 y)}{2} + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.2.3

Multiply $3$ by $- 5$ .

$\frac{65}{2} + \frac{- 15 y}{2} + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{65}{2} + \frac{- 15 y}{2} + 5 (- \frac{7 z}{2}) + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.3

Multiply $5 (- \frac{7 z}{2})$ .

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Step 2.4.1.1.2.3.1

Multiply $- 1$ by $5$ .

$\frac{65}{2} + \frac{- 15 y}{2} - 5 \frac{7 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.3.2

Combine $- 5$ and $\frac{7 z}{2}$ .

$\frac{65}{2} + \frac{- 15 y}{2} + \frac{- 5 (7 z)}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.2.3.3

Multiply $7$ by $- 5$ .

$\frac{65}{2} + \frac{- 15 y}{2} + \frac{- 35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{65}{2} + \frac{- 15 y}{2} + \frac{- 35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{65}{2} + \frac{- 15 y}{2} + \frac{- 35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.3

Simplify each term.

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Step 2.4.1.1.3.1

Move the negative in front of the fraction.

$\frac{65}{2} - \frac{15 y}{2} + \frac{- 35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.1.3.2

Move the negative in front of the fraction.

$\frac{65}{2} - \frac{15 y}{2} - \frac{35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{65}{2} - \frac{15 y}{2} - \frac{35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{65}{2} - \frac{15 y}{2} - \frac{35 z}{2} + 7 y - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.2

To write $7 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{65}{2} - \frac{35 z}{2} - \frac{15 y}{2} + 7 y \cdot \frac{2}{2} - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.3

Combine $7 y$ and $\frac{2}{2}$ .

$\frac{65}{2} - \frac{35 z}{2} - \frac{15 y}{2} + \frac{7 y \cdot 2}{2} - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.4

Combine the numerators over the common denominator.

$\frac{65}{2} - \frac{35 z}{2} + \frac{- 15 y + 7 y \cdot 2}{2} - 3 z = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.5

Combine the numerators over the common denominator.

$- 3 z + \frac{65 - 35 z - 15 y + 7 y \cdot 2}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.6

Multiply $2$ by $7$ .

$- 3 z + \frac{65 - 35 z - 15 y + 14 y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.7

Add $- 15 y$ and $14 y$ .

$- 3 z + \frac{65 - 35 z - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.8

To write $- 3 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 3 z \cdot \frac{2}{2} + \frac{65 - 35 z - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.9

Simplify terms.

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Step 2.4.1.9.1

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

$\frac{- 3 z \cdot 2}{2} + \frac{65 - 35 z - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.9.2

Combine the numerators over the common denominator.

$\frac{- 3 z \cdot 2 + 65 - 35 z - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{- 3 z \cdot 2 + 65 - 35 z - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.10

Simplify the numerator.

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Step 2.4.1.10.1

Multiply $2$ by $- 3$ .

$\frac{- 6 z + 65 - 35 z - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.10.2

Subtract $35 z$ from $- 6 z$ .

$\frac{- 41 z + 65 - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$\frac{- 41 z + 65 - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11

Simplify with factoring out.

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Step 2.4.1.11.1

Factor $- 1$ out of $- 41 z$ .

$\frac{- (41 z) + 65 - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11.2

Rewrite $65$ as $- 1 (- 65)$ .

$\frac{- (41 z) - 1 \cdot - 65 - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11.3

Factor $- 1$ out of $- (41 z) - 1 (- 65)$ .

$\frac{- (41 z - 65) - y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11.4

Factor $- 1$ out of $- y$ .

$\frac{- (41 z - 65) - (y)}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11.5

Factor $- 1$ out of $- (41 z - 65) - (y)$ .

$\frac{- (41 z - 65 + y)}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11.6

Simplify the expression.

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Step 2.4.1.11.6.1

Rewrite $- (41 z - 65 + y)$ as $- 1 (41 z - 65 + y)$ .

$\frac{- 1 (41 z - 65 + y)}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 2.4.1.11.6.2

Move the negative in front of the fraction.

$- \frac{41 z - 65 + y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{41 z - 65 + y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{41 z - 65 + y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{41 z - 65 + y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{41 z - 65 + y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{41 z - 65 + y}{2} = - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3

Solve for $y$ in $- \frac{41 z - 65 + y}{2} = - 28$ .

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Step 3.1

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{41 z - 65 + y}{2}) = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2

Simplify both sides of the equation.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $- 2 (- \frac{41 z - 65 + y}{2})$ .

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Step 3.2.1.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1.1

Move the leading negative in $- \frac{41 z - 65 + y}{2}$ into the numerator.

$- 2 \frac{- (41 z - 65 + y)}{2} = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) (\frac{- (41 z - 65 + y)}{2}) = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2.1.1.1.3

Cancel the common factor.

$2 \cdot (- 1 \frac{- (41 z - 65 + y)}{2}) = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2.1.1.1.4

Rewrite the expression.

$41 z - 65 + y = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$41 z - 65 + y = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2.1.1.2

Multiply.

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Step 3.2.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (41 z - 65 + y) = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2.1.1.2.2

Multiply $41 z - 65 + y$ by $1$ .

$41 z - 65 + y = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$41 z - 65 + y = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$41 z - 65 + y = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$41 z - 65 + y = - 2 \cdot - 28$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $- 2$ by $- 28$ .

$41 z - 65 + y = 56$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$41 z - 65 + y = 56$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$41 z - 65 + y = 56$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.3

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

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Step 3.3.1

Subtract $41 z$ from both sides of the equation.

$- 65 + y = 56 - 41 z$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.3.2

Add $65$ to both sides of the equation.

$y = 56 - 41 z + 65$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 3.3.3

Add $56$ and $65$ .

$y = - 41 z + 121$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$y = - 41 z + 121$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$y = - 41 z + 121$

$- \frac{31 z - 39 + 5 y}{2} = - 22$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4

Replace all occurrences of $y$ with $- 41 z + 121$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $- \frac{31 z - 39 + 5 y}{2} = - 22$ with $- 41 z + 121$ .

$- \frac{31 z - 39 + 5 (- 41 z + 121)}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $- \frac{31 z - 39 + 5 (- 41 z + 121)}{2}$ .

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Step 4.2.1.1

Simplify the numerator.

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Step 4.2.1.1.1

Apply the distributive property.

$- \frac{31 z - 39 + 5 (- 41 z) + 5 \cdot 121}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.2

Multiply $- 41$ by $5$ .

$- \frac{31 z - 39 - 205 z + 5 \cdot 121}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.3

Multiply $5$ by $121$ .

$- \frac{31 z - 39 - 205 z + 605}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.4

Subtract $205 z$ from $31 z$ .

$- \frac{- 174 z - 39 + 605}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.5

Add $- 39$ and $605$ .

$- \frac{- 174 z + 566}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.6

Factor $2$ out of $- 174 z + 566$ .

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Step 4.2.1.1.6.1

Factor $2$ out of $- 174 z$ .

$- \frac{2 (- 87 z) + 566}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.6.2

Factor $2$ out of $566$ .

$- \frac{2 (- 87 z) + 2 (283)}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.1.6.3

Factor $2$ out of $2 (- 87 z) + 2 (283)$ .

$- \frac{2 (- 87 z + 283)}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{2 (- 87 z + 283)}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- \frac{2 (- 87 z + 283)}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.2

Simplify terms.

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Step 4.2.1.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.2.1.1

Cancel the common factor.

$- \frac{2 (- 87 z + 283)}{2} = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.2.1.2

Divide $- 87 z + 283$ by $1$ .

$- (- 87 z + 283) = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$- (- 87 z + 283) = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.2.2

Apply the distributive property.

$- (- 87 z) - 1 \cdot 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.2.3

Multiply.

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Step 4.2.1.2.3.1

Multiply $- 87$ by $- 1$ .

$87 z - 1 \cdot 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.2.1.2.3.2

Multiply $- 1$ by $283$ .

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$

Step 4.3

Replace all occurrences of $y$ in $x = \frac{13}{2} - \frac{3 y}{2} - \frac{7 z}{2}$ with $- 41 z + 121$ .

$x = \frac{13}{2} - \frac{3 (- 41 z + 121)}{2} - \frac{7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $\frac{13}{2} - \frac{3 (- 41 z + 121)}{2} - \frac{7 z}{2}$ .

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Step 4.4.1.1

Combine the numerators over the common denominator.

$x = \frac{13 - 3 (- 41 z + 121) - 7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.2

Simplify each term.

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Step 4.4.1.2.1

Apply the distributive property.

$x = \frac{13 - 3 (- 41 z) - 3 \cdot 121 - 7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.2.2

Multiply $- 41$ by $- 3$ .

$x = \frac{13 + 123 z - 3 \cdot 121 - 7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.2.3

Multiply $- 3$ by $121$ .

$x = \frac{13 + 123 z - 363 - 7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = \frac{13 + 123 z - 363 - 7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3

Simplify terms.

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Step 4.4.1.3.1

Subtract $363$ from $13$ .

$x = \frac{123 z - 350 - 7 z}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.2

Subtract $7 z$ from $123 z$ .

$x = \frac{116 z - 350}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3

Cancel the common factor of $116 z - 350$ and $2$ .

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Step 4.4.1.3.3.1

Factor $2$ out of $116 z$ .

$x = \frac{2 (58 z) - 350}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3.2

Factor $2$ out of $- 350$ .

$x = \frac{2 (58 z) + 2 \cdot - 175}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3.3

Factor $2$ out of $2 (58 z) + 2 (- 175)$ .

$x = \frac{2 (58 z - 175)}{2}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3.4

Cancel the common factors.

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Step 4.4.1.3.3.4.1

Factor $2$ out of $2$ .

$x = \frac{2 (58 z - 175)}{2 (1)}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3.4.2

Cancel the common factor.

$x = \frac{2 (58 z - 175)}{2 \cdot 1}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3.4.3

Rewrite the expression.

$x = \frac{58 z - 175}{1}$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 4.4.1.3.3.4.4

Divide $58 z - 175$ by $1$ .

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

$x = 58 z - 175$

$87 z - 283 = - 22$

$y = - 41 z + 121$

Step 5

Solve for $z$ in $87 z - 283 = - 22$ .

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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 $283$ to both sides of the equation.

$87 z = - 22 + 283$

$x = 58 z - 175$

$y = - 41 z + 121$

Step 5.1.2

Add $- 22$ and $283$ .

$87 z = 261$

$x = 58 z - 175$

$y = - 41 z + 121$

$87 z = 261$

$x = 58 z - 175$

$y = - 41 z + 121$

Step 5.2

Divide each term in $87 z = 261$ by $87$ and simplify.

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Step 5.2.1

Divide each term in $87 z = 261$ by $87$ .

$\frac{87 z}{87} = \frac{261}{87}$

$x = 58 z - 175$

$y = - 41 z + 121$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $87$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{87 z}{87} = \frac{261}{87}$

$x = 58 z - 175$

$y = - 41 z + 121$

Step 5.2.2.1.2

Divide $z$ by $1$ .

$z = \frac{261}{87}$

$x = 58 z - 175$

$y = - 41 z + 121$

$z = \frac{261}{87}$

$x = 58 z - 175$

$y = - 41 z + 121$

$z = \frac{261}{87}$

$x = 58 z - 175$

$y = - 41 z + 121$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $261$ by $87$ .

$z = 3$

$x = 58 z - 175$

$y = - 41 z + 121$

$z = 3$

$x = 58 z - 175$

$y = - 41 z + 121$

$z = 3$

$x = 58 z - 175$

$y = - 41 z + 121$

$z = 3$

$x = 58 z - 175$

$y = - 41 z + 121$

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 $x = 58 z - 175$ with $3$ .

$x = 58 (3) - 175$

$z = 3$

$y = - 41 z + 121$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $58 (3) - 175$ .

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Step 6.2.1.1

Multiply $58$ by $3$ .

$x = 174 - 175$

$z = 3$

$y = - 41 z + 121$

Step 6.2.1.2

Subtract $175$ from $174$ .

$x = - 1$

$z = 3$

$y = - 41 z + 121$

$x = - 1$

$z = 3$

$y = - 41 z + 121$

$x = - 1$

$z = 3$

$y = - 41 z + 121$

Step 6.3

Replace all occurrences of $z$ in $y = - 41 z + 121$ with $3$ .

$y = - 41 \cdot 3 + 121$

$x = - 1$

$z = 3$

Step 6.4

Simplify the right side.

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Step 6.4.1

Simplify $- 41 \cdot 3 + 121$ .

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Step 6.4.1.1

Multiply $- 41$ by $3$ .

$y = - 123 + 121$

$x = - 1$

$z = 3$

Step 6.4.1.2

Add $- 123$ and $121$ .

$y = - 2$

$x = - 1$

$z = 3$

$y = - 2$

$x = - 1$

$z = 3$

$y = - 2$

$x = - 1$

$z = 3$

$y = - 2$

$x = - 1$

$z = 3$

Step 7

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

$(- 1, - 2, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(- 1, - 2, 3)$

Equation Form:

$x = - 1, y = - 2, z = 3$