Algebra Examples

$18 x - 9 y + 3 z = 18$

Step 1

Solve the equation for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $18 x$ from both sides of the equation.

$- 9 y + 3 z = 18 - 18 x$

Step 1.1.2

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

$- 9 y = 18 - 18 x - 3 z$

Step 1.2

Divide each term in $- 9 y = 18 - 18 x - 3 z$ by $- 9$ and simplify.

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Step 1.2.1

Divide each term in $- 9 y = 18 - 18 x - 3 z$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{18}{- 9} + \frac{- 18 x}{- 9} + \frac{- 3 z}{- 9}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 9$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{18}{- 9} + \frac{- 18 x}{- 9} + \frac{- 3 z}{- 9}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{- 9} + \frac{- 18 x}{- 9} + \frac{- 3 z}{- 9}$

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

Divide $18$ by $- 9$ .

$y = - 2 + \frac{- 18 x}{- 9} + \frac{- 3 z}{- 9}$

Step 1.2.3.1.2

Cancel the common factor of $- 18$ and $- 9$ .

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Step 1.2.3.1.2.1

Factor $- 9$ out of $- 18 x$ .

$y = - 2 + \frac{- 9 (2 x)}{- 9} + \frac{- 3 z}{- 9}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $- 9$ out of $- 9$ .

$y = - 2 + \frac{- 9 (2 x)}{- 9 (1)} + \frac{- 3 z}{- 9}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = - 2 + \frac{- 9 (2 x)}{- 9 \cdot 1} + \frac{- 3 z}{- 9}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = - 2 + \frac{2 x}{1} + \frac{- 3 z}{- 9}$

Step 1.2.3.1.2.2.4

Divide $2 x$ by $1$ .

$y = - 2 + 2 x + \frac{- 3 z}{- 9}$

Step 1.2.3.1.3

Cancel the common factor of $- 3$ and $- 9$ .

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Step 1.2.3.1.3.1

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

$y = - 2 + 2 x + \frac{- 3 (z)}{- 9}$

Step 1.2.3.1.3.2

Cancel the common factors.

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Step 1.2.3.1.3.2.1

Factor $- 3$ out of $- 9$ .

$y = - 2 + 2 x + \frac{- 3 (z)}{- 3 (3)}$

Step 1.2.3.1.3.2.2

Cancel the common factor.

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

Step 1.2.3.1.3.2.3

Rewrite the expression.

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

Step 2

Choose any values for $x$ and $y$ that are in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ and $1$ to substitute for $z$ .

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Step 3.1

Remove parentheses.

$y = - 2 + 2 (0) + \frac{1}{3}$

Step 3.2

Simplify $- 2 + 2 (0) + \frac{1}{3}$ .

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Step 3.2.1

Multiply $2$ by $0$ .

$y = - 2 + 0 + \frac{1}{3}$

Step 3.2.2

Add $- 2$ and $0$ .

$y = - 2 + \frac{1}{3}$

Step 3.2.3

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

$y = - 2 \cdot \frac{3}{3} + \frac{1}{3}$

Step 3.2.4

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

$y = \frac{- 2 \cdot 3}{3} + \frac{1}{3}$

Step 3.2.5

Combine the numerators over the common denominator.

$y = \frac{- 2 \cdot 3 + 1}{3}$

Step 3.2.6

Simplify the numerator.

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Step 3.2.6.1

Multiply $- 2$ by $3$ .

$y = \frac{- 6 + 1}{3}$

Step 3.2.6.2

Add $- 6$ and $1$ .

$y = \frac{- 5}{3}$

Step 3.2.7

Move the negative in front of the fraction.

$y = - \frac{5}{3}$

Step 3.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(0, - \frac{5}{3}, 1)$

Step 4

Choose $1$ to substitute in for $x$ and $2$ to substitute for $z$ .

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Step 4.1

Remove parentheses.

$y = - 2 + 2 (1) + \frac{2}{3}$

Step 4.2

Simplify $- 2 + 2 (1) + \frac{2}{3}$ .

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Step 4.2.1

Multiply $2$ by $1$ .

$y = - 2 + 2 + \frac{2}{3}$

Step 4.2.2

Find the common denominator.

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Step 4.2.2.1

Write $- 2$ as a fraction with denominator $1$ .

$y = \frac{- 2}{1} + 2 + \frac{2}{3}$

Step 4.2.2.2

Multiply $\frac{- 2}{1}$ by $\frac{3}{3}$ .

$y = \frac{- 2}{1} \cdot \frac{3}{3} + 2 + \frac{2}{3}$

Step 4.2.2.3

Multiply $\frac{- 2}{1}$ by $\frac{3}{3}$ .

$y = \frac{- 2 \cdot 3}{3} + 2 + \frac{2}{3}$

Step 4.2.2.4

Write $2$ as a fraction with denominator $1$ .

$y = \frac{- 2 \cdot 3}{3} + \frac{2}{1} + \frac{2}{3}$

Step 4.2.2.5

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

$y = \frac{- 2 \cdot 3}{3} + \frac{2}{1} \cdot \frac{3}{3} + \frac{2}{3}$

Step 4.2.2.6

Multiply $\frac{2}{1}$ by $\frac{3}{3}$ .

$y = \frac{- 2 \cdot 3}{3} + \frac{2 \cdot 3}{3} + \frac{2}{3}$

Step 4.2.3

Combine the numerators over the common denominator.

$y = \frac{- 2 \cdot 3 + 2 \cdot 3 + 2}{3}$

Step 4.2.4

Simplify each term.

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Step 4.2.4.1

Multiply $- 2$ by $3$ .

$y = \frac{- 6 + 2 \cdot 3 + 2}{3}$

Step 4.2.4.2

Multiply $2$ by $3$ .

$y = \frac{- 6 + 6 + 2}{3}$

Step 4.2.5

Simplify by adding numbers.

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Step 4.2.5.1

Add $- 6$ and $6$ .

$y = \frac{0 + 2}{3}$

Step 4.2.5.2

Add $0$ and $2$ .

$y = \frac{2}{3}$

Step 4.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(1, \frac{2}{3}, 2)$

Step 5

Choose $2$ to substitute in for $x$ and $3$ to substitute for $z$ .

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Step 5.1

Remove parentheses.

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

Step 5.2

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

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Multiply $2$ by $2$ .

$y = - 2 + 4 + \frac{3}{3}$

Step 5.2.1.2

Divide $3$ by $3$ .

$y = - 2 + 4 + 1$

Step 5.2.2

Simplify by adding numbers.

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Step 5.2.2.1

Add $- 2$ and $4$ .

$y = 2 + 1$

Step 5.2.2.2

Add $2$ and $1$ .

$y = 3$

Step 5.3

Use the $x$ , $y$ , and $z$ values to form the ordered pair.

$(2, 3, 3)$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{5}{3}, 1), (1, \frac{2}{3}, 2), (2, 3, 3)$