Algebra Examples

$2 x - 4 y + 2 z = 4$ $x + 2 y - 4 z = 8$ $3 x - 6 y + 3 z = 8$

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.

$x - 4 z = 8 - 2 y$

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

$3 x - 6 y + 3 z = 8$

Step 1.2

Add $4 z$ to both sides of the equation.

$x = 8 - 2 y + 4 z$

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

$3 x - 6 y + 3 z = 8$

$x = 8 - 2 y + 4 z$

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

$3 x - 6 y + 3 z = 8$

Step 2

Replace all occurrences of $x$ with $8 - 2 y + 4 z$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2 x - 4 y + 2 z = 4$ with $8 - 2 y + 4 z$ .

$2 (8 - 2 y + 4 z) - 4 y + 2 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (8 - 2 y + 4 z) - 4 y + 2 z$ .

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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.

$2 \cdot 8 + 2 (- 2 y) + 2 (4 z) - 4 y + 2 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.2.1.1.2

Simplify.

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Step 2.2.1.1.2.1

Multiply $2$ by $8$ .

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

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.2.1.1.2.2

Multiply $- 2$ by $2$ .

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

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.2.1.1.2.3

Multiply $4$ by $2$ .

$16 - 4 y + 8 z - 4 y + 2 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

$16 - 4 y + 8 z - 4 y + 2 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

$16 - 4 y + 8 z - 4 y + 2 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

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

$16 - 8 y + 8 z + 2 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.2.1.2.2

Add $8 z$ and $2 z$ .

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$3 x - 6 y + 3 z = 8$

Step 2.3

Replace all occurrences of $x$ in $3 x - 6 y + 3 z = 8$ with $8 - 2 y + 4 z$ .

$3 (8 - 2 y + 4 z) - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 2.4

Simplify the left side.

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Step 2.4.1

Simplify $3 (8 - 2 y + 4 z) - 6 y + 3 z$ .

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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.

$3 \cdot 8 + 3 (- 2 y) + 3 (4 z) - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 2.4.1.1.2

Simplify.

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Step 2.4.1.1.2.1

Multiply $3$ by $8$ .

$24 + 3 (- 2 y) + 3 (4 z) - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 2.4.1.1.2.2

Multiply $- 2$ by $3$ .

$24 - 6 y + 3 (4 z) - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 2.4.1.1.2.3

Multiply $4$ by $3$ .

$24 - 6 y + 12 z - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$24 - 6 y + 12 z - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$24 - 6 y + 12 z - 6 y + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 2.4.1.2

Simplify by adding terms.

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Step 2.4.1.2.1

Subtract $6 y$ from $- 6 y$ .

$24 - 12 y + 12 z + 3 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 2.4.1.2.2

Add $12 z$ and $3 z$ .

$24 - 12 y + 15 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$24 - 12 y + 15 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$24 - 12 y + 15 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$24 - 12 y + 15 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$24 - 12 y + 15 z = 8$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3

Solve for $y$ in $24 - 12 y + 15 z = 8$ .

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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.

$- 12 y + 15 z = 8 - 24$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.1.2

Subtract $15 z$ from both sides of the equation.

$- 12 y = 8 - 24 - 15 z$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.1.3

Subtract $24$ from $8$ .

$- 12 y = - 16 - 15 z$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$- 12 y = - 16 - 15 z$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2

Divide each term in $- 12 y = - 16 - 15 z$ by $- 12$ and simplify.

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Step 3.2.1

Divide each term in $- 12 y = - 16 - 15 z$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{- 16}{- 12} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 12$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{- 16}{- 12} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 16}{- 12} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{- 16}{- 12} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{- 16}{- 12} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

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

Cancel the common factor of $- 16$ and $- 12$ .

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Step 3.2.3.1.1.1

Factor $- 4$ out of $- 16$ .

$y = \frac{- 4 \cdot 4}{- 12} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.1.2

Cancel the common factors.

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Step 3.2.3.1.1.2.1

Factor $- 4$ out of $- 12$ .

$y = \frac{- 4 \cdot 4}{- 4 \cdot 3} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 4 \cdot 4}{- 4 \cdot 3} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{4}{3} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{- 15 z}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.2

Cancel the common factor of $- 15$ and $- 12$ .

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Step 3.2.3.1.2.1

Factor $- 3$ out of $- 15 z$ .

$y = \frac{4}{3} + \frac{- 3 (5 z)}{- 12}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.2.2

Cancel the common factors.

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Step 3.2.3.1.2.2.1

Factor $- 3$ out of $- 12$ .

$y = \frac{4}{3} + \frac{- 3 (5 z)}{- 3 \cdot 4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{4}{3} + \frac{- 3 (5 z)}{- 3 \cdot 4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 3.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

$y = \frac{4}{3} + \frac{5 z}{4}$

$16 - 8 y + 10 z = 4$

$x = 8 - 2 y + 4 z$

Step 4

Replace all occurrences of $y$ with $\frac{4}{3} + \frac{5 z}{4}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $16 - 8 y + 10 z = 4$ with $\frac{4}{3} + \frac{5 z}{4}$ .

$16 - 8 (\frac{4}{3} + \frac{5 z}{4}) + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify $16 - 8 (\frac{4}{3} + \frac{5 z}{4}) + 10 z$ .

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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.

$16 - 8 (\frac{4}{3}) - 8 \frac{5 z}{4} + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.2

Multiply $- 8 (\frac{4}{3})$ .

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Step 4.2.1.1.2.1

Combine $- 8$ and $\frac{4}{3}$ .

$16 + \frac{- 8 \cdot 4}{3} - 8 \frac{5 z}{4} + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.2.2

Multiply $- 8$ by $4$ .

$16 + \frac{- 32}{3} - 8 \frac{5 z}{4} + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$16 + \frac{- 32}{3} - 8 \frac{5 z}{4} + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.3

Cancel the common factor of $4$ .

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Step 4.2.1.1.3.1

Factor $4$ out of $- 8$ .

$16 + \frac{- 32}{3} + 4 (- 2) (\frac{5 z}{4}) + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.3.2

Cancel the common factor.

$16 + \frac{- 32}{3} + 4 \cdot (- 2 \frac{5 z}{4}) + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.3.3

Rewrite the expression.

$16 + \frac{- 32}{3} - 2 (5 z) + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$16 + \frac{- 32}{3} - 2 (5 z) + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.4

Multiply $5$ by $- 2$ .

$16 + \frac{- 32}{3} - 10 z + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.1.5

Move the negative in front of the fraction.

$16 - \frac{32}{3} - 10 z + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$16 - \frac{32}{3} - 10 z + 10 z = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.2

Combine the opposite terms in $16 - \frac{32}{3} - 10 z + 10 z$ .

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Step 4.2.1.2.1

Add $- 10 z$ and $10 z$ .

$16 - \frac{32}{3} + 0 = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.2.2

Add $16 - \frac{32}{3}$ and $0$ .

$16 - \frac{32}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$16 - \frac{32}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.3

To write $16$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$16 \cdot \frac{3}{3} - \frac{32}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.4

Combine $16$ and $\frac{3}{3}$ .

$\frac{16 \cdot 3}{3} - \frac{32}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.5

Combine the numerators over the common denominator.

$\frac{16 \cdot 3 - 32}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.6

Simplify the numerator.

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Step 4.2.1.6.1

Multiply $16$ by $3$ .

$\frac{48 - 32}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.2.1.6.2

Subtract $32$ from $48$ .

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - 2 y + 4 z$

Step 4.3

Replace all occurrences of $y$ in $x = 8 - 2 y + 4 z$ with $\frac{4}{3} + \frac{5 z}{4}$ .

$x = 8 - 2 (\frac{4}{3} + \frac{5 z}{4}) + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4

Simplify the right side.

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Step 4.4.1

Simplify $8 - 2 (\frac{4}{3} + \frac{5 z}{4}) + 4 z$ .

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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.

$x = 8 - 2 (\frac{4}{3}) - 2 \frac{5 z}{4} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.2

Multiply $- 2 (\frac{4}{3})$ .

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Step 4.4.1.1.2.1

Combine $- 2$ and $\frac{4}{3}$ .

$x = 8 + \frac{- 2 \cdot 4}{3} - 2 \frac{5 z}{4} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.2.2

Multiply $- 2$ by $4$ .

$x = 8 + \frac{- 8}{3} - 2 \frac{5 z}{4} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 + \frac{- 8}{3} - 2 \frac{5 z}{4} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.3

Cancel the common factor of $2$ .

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Step 4.4.1.1.3.1

Factor $2$ out of $- 2$ .

$x = 8 + \frac{- 8}{3} + 2 (- 1) (\frac{5 z}{4}) + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.3.2

Factor $2$ out of $4$ .

$x = 8 + \frac{- 8}{3} + 2 \cdot (- 1 \frac{5 z}{2 \cdot 2}) + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.3.3

Cancel the common factor.

$x = 8 + \frac{- 8}{3} + 2 \cdot (- 1 \frac{5 z}{2 \cdot 2}) + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.3.4

Rewrite the expression.

$x = 8 + \frac{- 8}{3} - 1 \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 + \frac{- 8}{3} - 1 \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.4

Simplify each term.

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Step 4.4.1.1.4.1

Move the negative in front of the fraction.

$x = 8 - \frac{8}{3} - 1 \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.1.4.2

Rewrite $- 1 \frac{5 z}{2}$ as $- \frac{5 z}{2}$ .

$x = 8 - \frac{8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - \frac{8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = 8 - \frac{8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 8 \cdot \frac{3}{3} - \frac{8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.3

Combine $8$ and $\frac{3}{3}$ .

$x = \frac{8 \cdot 3}{3} - \frac{8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.4

Combine the numerators over the common denominator.

$x = \frac{8 \cdot 3 - 8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.5

Simplify the numerator.

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Step 4.4.1.5.1

Multiply $8$ by $3$ .

$x = \frac{24 - 8}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.5.2

Subtract $8$ from $24$ .

$x = \frac{16}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} - \frac{5 z}{2} + 4 z$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.6

To write $4 z$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{16}{3} - \frac{5 z}{2} + 4 z \cdot \frac{2}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.7

Simplify terms.

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Step 4.4.1.7.1

Combine $4 z$ and $\frac{2}{2}$ .

$x = \frac{16}{3} - \frac{5 z}{2} + \frac{4 z \cdot 2}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.7.2

Combine the numerators over the common denominator.

$x = \frac{16}{3} + \frac{- 5 z + 4 z \cdot 2}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{- 5 z + 4 z \cdot 2}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.8

Simplify each term.

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Step 4.4.1.8.1

Simplify the numerator.

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Step 4.4.1.8.1.1

Factor $z$ out of $- 5 z + 4 z \cdot 2$ .

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Step 4.4.1.8.1.1.1

Factor $z$ out of $- 5 z$ .

$x = \frac{16}{3} + \frac{z \cdot - 5 + 4 z \cdot 2}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.8.1.1.2

Factor $z$ out of $4 z \cdot 2$ .

$x = \frac{16}{3} + \frac{z \cdot - 5 + z (4 \cdot 2)}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.8.1.1.3

Factor $z$ out of $z \cdot - 5 + z (4 \cdot 2)$ .

$x = \frac{16}{3} + \frac{z (- 5 + 4 \cdot 2)}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{z (- 5 + 4 \cdot 2)}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.8.1.2

Multiply $4$ by $2$ .

$x = \frac{16}{3} + \frac{z (- 5 + 8)}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.8.1.3

Add $- 5$ and $8$ .

$x = \frac{16}{3} + \frac{z \cdot 3}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{z \cdot 3}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 4.4.1.8.2

Move $3$ to the left of $z$ .

$x = \frac{16}{3} + \frac{3 z}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{3 z}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{3 z}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{3 z}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

$x = \frac{16}{3} + \frac{3 z}{2}$

$\frac{16}{3} = 4$

$y = \frac{4}{3} + \frac{5 z}{4}$

Step 5

Since $\frac{16}{3} = 4$ is not true, there is no solution.

No solution