Algebra Examples

$7 x - 2 y - 14 z = 56$

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 $7 x$ from both sides of the equation.

$- 2 y - 14 z = 56 - 7 x$

Step 1.1.2

Add $14 z$ to both sides of the equation.

$- 2 y = 56 - 7 x + 14 z$

Step 1.2

Divide each term in $- 2 y = 56 - 7 x + 14 z$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 y = 56 - 7 x + 14 z$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{56}{- 2} + \frac{- 7 x}{- 2} + \frac{14 z}{- 2}$

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.

$\frac{- 2 y}{- 2} = \frac{56}{- 2} + \frac{- 7 x}{- 2} + \frac{14 z}{- 2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{56}{- 2} + \frac{- 7 x}{- 2} + \frac{14 z}{- 2}$

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 $56$ by $- 2$ .

$y = - 28 + \frac{- 7 x}{- 2} + \frac{14 z}{- 2}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = - 28 + \frac{7 x}{2} + \frac{14 z}{- 2}$

Step 1.2.3.1.3

Cancel the common factor of $14$ and $- 2$ .

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Step 1.2.3.1.3.1

Factor $2$ out of $14 z$ .

$y = - 28 + \frac{7 x}{2} + \frac{2 (7 z)}{- 2}$

Step 1.2.3.1.3.2

Move the negative one from the denominator of $\frac{7 z}{- 1}$ .

$y = - 28 + \frac{7 x}{2} - 1 \cdot (7 z)$

Step 1.2.3.1.4

Rewrite $- 1 \cdot (7 z)$ as $- (7 z)$ .

$y = - 28 + \frac{7 x}{2} - (7 z)$

Step 1.2.3.1.5

Multiply $7$ by $- 1$ .

$y = - 28 + \frac{7 x}{2} - 7 z$

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.

$y = - 28 + \frac{7 (0)}{2} - 7 \cdot 1$

Step 3.2

Simplify $- 28 + \frac{7 (0)}{2} - 7 \cdot 1$ .

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Step 3.2.1

Multiply $7$ by $0$ .

$y = - 28 + \frac{0}{2} - 7 \cdot 1$

Step 3.2.2

Simplify each term.

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Step 3.2.2.1

Divide $0$ by $2$ .

$y = - 28 + 0 - 7 \cdot 1$

Step 3.2.2.2

Multiply $- 7$ by $1$ .

$y = - 28 + 0 - 7$

Step 3.2.3

Simplify by adding and subtracting.

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Step 3.2.3.1

Add $- 28$ and $0$ .

$y = - 28 - 7$

Step 3.2.3.2

Subtract $7$ from $- 28$ .

$y = - 35$

Step 3.3

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

$(0, - 35, 1)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = - 28 + \frac{7 (1)}{2} - 7 \cdot 2$

Step 4.2

Simplify $- 28 + \frac{7 (1)}{2} - 7 \cdot 2$ .

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Step 4.2.1

Multiply $7$ by $1$ .

$y = - 28 + \frac{7}{2} - 7 \cdot 2$

Step 4.2.2

Multiply $- 7$ by $2$ .

$y = - 28 + \frac{7}{2} - 14$

Step 4.2.3

Find the common denominator.

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Step 4.2.3.1

Write $- 28$ as a fraction with denominator $1$ .

$y = \frac{- 28}{1} + \frac{7}{2} - 14$

Step 4.2.3.2

Multiply $\frac{- 28}{1}$ by $\frac{2}{2}$ .

$y = \frac{- 28}{1} \cdot \frac{2}{2} + \frac{7}{2} - 14$

Step 4.2.3.3

Multiply $\frac{- 28}{1}$ by $\frac{2}{2}$ .

$y = \frac{- 28 \cdot 2}{2} + \frac{7}{2} - 14$

Step 4.2.3.4

Write $- 14$ as a fraction with denominator $1$ .

$y = \frac{- 28 \cdot 2}{2} + \frac{7}{2} + \frac{- 14}{1}$

Step 4.2.3.5

Multiply $\frac{- 14}{1}$ by $\frac{2}{2}$ .

$y = \frac{- 28 \cdot 2}{2} + \frac{7}{2} + \frac{- 14}{1} \cdot \frac{2}{2}$

Step 4.2.3.6

Multiply $\frac{- 14}{1}$ by $\frac{2}{2}$ .

$y = \frac{- 28 \cdot 2}{2} + \frac{7}{2} + \frac{- 14 \cdot 2}{2}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{- 28 \cdot 2 + 7 - 14 \cdot 2}{2}$

Step 4.2.5

Simplify each term.

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Step 4.2.5.1

Multiply $- 28$ by $2$ .

$y = \frac{- 56 + 7 - 14 \cdot 2}{2}$

Step 4.2.5.2

Multiply $- 14$ by $2$ .

$y = \frac{- 56 + 7 - 28}{2}$

Step 4.2.6

Simplify the expression.

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Step 4.2.6.1

Add $- 56$ and $7$ .

$y = \frac{- 49 - 28}{2}$

Step 4.2.6.2

Subtract $28$ from $- 49$ .

$y = \frac{- 77}{2}$

Step 4.2.6.3

Move the negative in front of the fraction.

$y = - \frac{77}{2}$

Step 4.3

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

$(1, - \frac{77}{2}, 2)$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

Simplify $- 28 + \frac{7 (2)}{2} - 7 \cdot 3$ .

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Step 5.2.1

Multiply $7$ by $2$ .

$y = - 28 + \frac{14}{2} - 7 \cdot 3$

Step 5.2.2

Simplify each term.

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Step 5.2.2.1

Divide $14$ by $2$ .

$y = - 28 + 7 - 7 \cdot 3$

Step 5.2.2.2

Multiply $- 7$ by $3$ .

$y = - 28 + 7 - 21$

Step 5.2.3

Simplify by adding and subtracting.

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Step 5.2.3.1

Add $- 28$ and $7$ .

$y = - 21 - 21$

Step 5.2.3.2

Subtract $21$ from $- 21$ .

$y = - 42$

Step 5.3

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

$(2, - 42, 3)$

Step 6

These are three possible solutions to the equation.

$(0, - 35, 1), (1, - \frac{77}{2}, 2), (2, - 42, 3)$