Precalculus Examples

$x + 2 y - z = - 3$ , $2 x + 3 y - 4 z = - 33$ , $3 x + k y - 4 z = - 8$

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.

$x - z = - 3 - 2 y$

$2 x + 3 y - 4 z = - 33$

$3 x + k y - 4 z = - 8$

Step 1.2

Add $z$ to both sides of the equation.

$x = - 3 - 2 y + z$

$2 x + 3 y - 4 z = - 33$

$3 x + k y - 4 z = - 8$

$x = - 3 - 2 y + z$

$2 x + 3 y - 4 z = - 33$

$3 x + k y - 4 z = - 8$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $2 (- 3 - 2 y + z) + 3 y - 4 z$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Apply the distributive property.

$2 \cdot - 3 + 2 (- 2 y) + 2 z + 3 y - 4 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.1.1.2

Simplify.

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Step 2.1.1.2.1

Multiply $2$ by $- 3$ .

$- 6 + 2 (- 2 y) + 2 z + 3 y - 4 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.1.1.2.2

Multiply $- 2$ by $2$ .

$- 6 - 4 y + 2 z + 3 y - 4 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$- 6 - 4 y + 2 z + 3 y - 4 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$- 6 - 4 y + 2 z + 3 y - 4 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.1.2

Simplify by adding terms.

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Step 2.1.2.1

Add $- 4 y$ and $3 y$ .

$- 6 - y + 2 z - 4 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.1.2.2

Subtract $4 z$ from $2 z$ .

$- 6 - y - 2 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$- 6 - y - 2 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$- 6 - y - 2 z = - 33$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.2

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

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Step 2.2.1

Add $6$ to both sides of the equation.

$- y - 2 z = - 33 + 6$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.2.2

Add $2 z$ to both sides of the equation.

$- y = - 33 + 6 + 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.2.3

Add $- 33$ and $6$ .

$- y = - 27 + 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$- y = - 27 + 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3

Divide each term in $- y = - 27 + 2 z$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- y = - 27 + 2 z$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 27}{- 1} + \frac{2 z}{- 1}$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 27}{- 1} + \frac{2 z}{- 1}$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3.2.2

Divide $y$ by $1$ .

$y = \frac{- 27}{- 1} + \frac{2 z}{- 1}$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$y = \frac{- 27}{- 1} + \frac{2 z}{- 1}$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Divide $- 27$ by $- 1$ .

$y = 27 + \frac{2 z}{- 1}$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3.3.1.2

Move the negative one from the denominator of $\frac{2 z}{- 1}$ .

$y = 27 - 1 \cdot (2 z)$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3.3.1.3

Rewrite $- 1 \cdot (2 z)$ as $- (2 z)$ .

$y = 27 - (2 z)$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 2.3.3.1.4

Multiply $2$ by $- 1$ .

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$3 x + k y - 4 z = - 8$

Step 3

Solve the equation for $z$ .

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Step 3.1

Simplify $3 (- 3 - 2 (27 - 2 z) + z) + k (27 - 2 z) - 4 z$ .

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Step 3.1.1

Simplify each term.

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Step 3.1.1.1

Simplify each term.

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Step 3.1.1.1.1

Apply the distributive property.

$3 (- 3 - 2 \cdot 27 - 2 (- 2 z) + z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.1.2

Multiply $- 2$ by $27$ .

$3 (- 3 - 54 - 2 (- 2 z) + z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.1.3

Multiply $- 2$ by $- 2$ .

$3 (- 3 - 54 + 4 z + z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$3 (- 3 - 54 + 4 z + z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.2

Subtract $54$ from $- 3$ .

$3 (- 57 + 4 z + z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.3

Add $4 z$ and $z$ .

$3 (- 57 + 5 z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.4

Apply the distributive property.

$3 \cdot - 57 + 3 (5 z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.5

Multiply $3$ by $- 57$ .

$- 171 + 3 (5 z) + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.6

Multiply $5$ by $3$ .

$- 171 + 15 z + k (27 - 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.7

Apply the distributive property.

$- 171 + 15 z + k \cdot 27 + k (- 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.8

Move $27$ to the left of $k$ .

$- 171 + 15 z + 27 \cdot k + k (- 2 z) - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.1.9

Rewrite using the commutative property of multiplication.

$- 171 + 15 z + 27 k - 2 k z - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$- 171 + 15 z + 27 k - 2 k z - 4 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.1.2

Subtract $4 z$ from $15 z$ .

$- 171 + 27 k - 2 k z + 11 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$- 171 + 27 k - 2 k z + 11 z = - 8$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.2

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

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Step 3.2.1

Add $171$ to both sides of the equation.

$27 k - 2 k z + 11 z = - 8 + 171$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.2.2

Subtract $27 k$ from both sides of the equation.

$- 2 k z + 11 z = - 8 + 171 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.2.3

Add $- 8$ and $171$ .

$- 2 k z + 11 z = 163 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$- 2 k z + 11 z = 163 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.3

Factor $z$ out of $- 2 k z + 11 z$ .

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Step 3.3.1

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

$z (- 2 k) + 11 z = 163 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.3.2

Factor $z$ out of $11 z$ .

$z (- 2 k) + z \cdot 11 = 163 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.3.3

Factor $z$ out of $z (- 2 k) + z \cdot 11$ .

$z (- 2 k + 11) = 163 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z (- 2 k + 11) = 163 - 27 k$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4

Divide each term in $z (- 2 k + 11) = 163 - 27 k$ by $- 2 k + 11$ and simplify.

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Step 3.4.1

Divide each term in $z (- 2 k + 11) = 163 - 27 k$ by $- 2 k + 11$ .

$\frac{z (- 2 k + 11)}{- 2 k + 11} = \frac{163}{- 2 k + 11} + \frac{- 27 k}{- 2 k + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $- 2 k + 11$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{z (- 2 k + 11)}{- 2 k + 11} = \frac{163}{- 2 k + 11} + \frac{- 27 k}{- 2 k + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.2.1.2

Divide $z$ by $1$ .

$z = \frac{163}{- 2 k + 11} + \frac{- 27 k}{- 2 k + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z = \frac{163}{- 2 k + 11} + \frac{- 27 k}{- 2 k + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z = \frac{163}{- 2 k + 11} + \frac{- 27 k}{- 2 k + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Combine the numerators over the common denominator.

$z = \frac{163 - 27 k}{- 2 k + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.3.2

Factor $- 1$ out of $- 2 k$ .

$z = \frac{163 - 27 k}{- (2 k) + 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.3.3

Rewrite $11$ as $- 1 (- 11)$ .

$z = \frac{163 - 27 k}{- (2 k) - 1 \cdot - 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.3.4

Factor $- 1$ out of $- (2 k) - 1 (- 11)$ .

$z = \frac{163 - 27 k}{- (2 k - 11)}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.3.5

Rewrite negatives.

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Step 3.4.3.5.1

Rewrite $- (2 k - 11)$ as $- 1 (2 k - 11)$ .

$z = \frac{163 - 27 k}{- 1 (2 k - 11)}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 3.4.3.5.2

Move the negative in front of the fraction.

$z = - \frac{163 - 27 k}{2 k - 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z = - \frac{163 - 27 k}{2 k - 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z = - \frac{163 - 27 k}{2 k - 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z = - \frac{163 - 27 k}{2 k - 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

$z = - \frac{163 - 27 k}{2 k - 11}$

$y = 27 - 2 z$

$x = - 3 - 2 y + z$

Step 4

Simplify the right side.

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Step 4.1

Simplify $27 - 2 (- \frac{163 - 27 k}{2 k - 11})$ .

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Step 4.1.1

Multiply $- 2 (- \frac{163 - 27 k}{2 k - 11})$ .

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Step 4.1.1.1

Multiply $- 1$ by $- 2$ .

$y = 27 + 2 (\frac{163 - 27 k}{2 k - 11})$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.1.2

Combine $2$ and $\frac{163 - 27 k}{2 k - 11}$ .

$y = 27 + \frac{2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

$y = 27 + \frac{2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.2

To write $27$ as a fraction with a common denominator, multiply by $\frac{2 k - 11}{2 k - 11}$ .

$y = 27 \cdot \frac{2 k - 11}{2 k - 11} + \frac{2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.3

Simplify terms.

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Step 4.1.3.1

Combine $27$ and $\frac{2 k - 11}{2 k - 11}$ .

$y = \frac{27 (2 k - 11)}{2 k - 11} + \frac{2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.3.2

Combine the numerators over the common denominator.

$y = \frac{27 (2 k - 11) + 2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

$y = \frac{27 (2 k - 11) + 2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4

Simplify the numerator.

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Step 4.1.4.1

Apply the distributive property.

$y = \frac{27 (2 k) + 27 \cdot - 11 + 2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.2

Multiply $2$ by $27$ .

$y = \frac{54 k + 27 \cdot - 11 + 2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.3

Multiply $27$ by $- 11$ .

$y = \frac{54 k - 297 + 2 (163 - 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.4

Apply the distributive property.

$y = \frac{54 k - 297 + 2 \cdot 163 + 2 (- 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.5

Multiply $2$ by $163$ .

$y = \frac{54 k - 297 + 326 + 2 (- 27 k)}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.6

Multiply $- 27$ by $2$ .

$y = \frac{54 k - 297 + 326 - 54 k}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.7

Subtract $54 k$ from $54 k$ .

$y = \frac{0 - 297 + 326}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.8

Subtract $297$ from $0$ .

$y = \frac{- 297 + 326}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 4.1.4.9

Add $- 297$ and $326$ .

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 y + z$

Step 5

Substitute the calculated values for $y, z$ into the equation for $x$ .

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Step 5.1

Simplify the left side.

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Step 5.1.1

Remove parentheses.

$x = - 3 - 2 \frac{29}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - 2 \frac{29}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 3 - 2 \frac{29}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$ .

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Step 5.2.1.1

Simplify each term.

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Step 5.2.1.1.1

Multiply $- 2 \frac{29}{2 k - 11}$ .

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Step 5.2.1.1.1.1

Combine $- 2$ and $\frac{29}{2 k - 11}$ .

$x = - 3 + \frac{- 2 \cdot 29}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.1.1.2

Multiply $- 2$ by $29$ .

$x = - 3 + \frac{- 58}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 + \frac{- 58}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.1.2

Move the negative in front of the fraction.

$x = - 3 - \frac{58}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 - \frac{58}{2 k - 11} - \frac{163 - 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.2

Combine the numerators over the common denominator.

$x = - 3 + \frac{- 58 - (163 - 27 k)}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.3

Simplify each term.

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Step 5.2.1.3.1

Apply the distributive property.

$x = - 3 + \frac{- 58 - 1 \cdot 163 - (- 27 k)}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.3.2

Multiply $- 1$ by $163$ .

$x = - 3 + \frac{- 58 - 163 - (- 27 k)}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.3.3

Multiply $- 27$ by $- 1$ .

$x = - 3 + \frac{- 58 - 163 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = - 3 + \frac{- 58 - 163 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.4

Subtract $163$ from $- 58$ .

$x = - 3 + \frac{- 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.5

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2 k - 11}{2 k - 11}$ .

$x = - 3 \cdot \frac{2 k - 11}{2 k - 11} + \frac{- 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.6

Simplify terms.

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Step 5.2.1.6.1

Combine $- 3$ and $\frac{2 k - 11}{2 k - 11}$ .

$x = \frac{- 3 (2 k - 11)}{2 k - 11} + \frac{- 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.6.2

Combine the numerators over the common denominator.

$x = \frac{- 3 (2 k - 11) - 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = \frac{- 3 (2 k - 11) - 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.7

Simplify the numerator.

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Step 5.2.1.7.1

Apply the distributive property.

$x = \frac{- 3 (2 k) - 3 \cdot - 11 - 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.7.2

Multiply $2$ by $- 3$ .

$x = \frac{- 6 k - 3 \cdot - 11 - 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.7.3

Multiply $- 3$ by $- 11$ .

$x = \frac{- 6 k + 33 - 221 + 27 k}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.7.4

Add $- 6 k$ and $27 k$ .

$x = \frac{21 k + 33 - 221}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

Step 5.2.1.7.5

Subtract $221$ from $33$ .

$x = \frac{21 k - 188}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = \frac{21 k - 188}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = \frac{21 k - 188}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = \frac{21 k - 188}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$

$x = \frac{21 k - 188}{2 k - 11}$

$y = \frac{29}{2 k - 11}$

$z = - \frac{163 - 27 k}{2 k - 11}$