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

Move the negative in front of the fraction.

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

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

Cancel the common factors.

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Step 1.2.3.1.3.2.1

Factor $2$ out of $2$ .

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

Step 1.2.3.1.3.2.2

Cancel the common factor.

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

Step 1.2.3.1.3.2.3

Rewrite the expression.

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

Step 1.2.3.1.3.2.4

Divide $7 z$ 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.

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

Step 3.2

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

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Step 3.2.1

Simplify each term.

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Step 3.2.1.1

Cancel the common factor of $0$ and $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $7 (0)$ .

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

Step 3.2.1.1.2

Cancel the common factors.

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Step 3.2.1.1.2.1

Factor $2$ out of $2$ .

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

Step 3.2.1.1.2.2

Cancel the common factor.

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

Step 3.2.1.1.2.3

Rewrite the expression.

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

Step 3.2.1.1.2.4

Divide $7 \cdot (0)$ by $1$ .

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

Step 3.2.1.2

Multiply $- (7 \cdot (0))$ .

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Step 3.2.1.2.1

Multiply $7$ by $0$ .

$y = 28 - 0 + 7 (1)$

Step 3.2.1.2.2

Multiply $- 1$ by $0$ .

$y = 28 + 0 + 7 (1)$

Step 3.2.1.3

Multiply $7$ by $1$ .

$y = 28 + 0 + 7$

Step 3.2.2

Simplify by adding numbers.

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Step 3.2.2.1

Add $28$ and $0$ .

$y = 28 + 7$

Step 3.2.2.2

Add $28$ and $7$ .

$y = 35$

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.

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

Step 4.2

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

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $7$ by $1$ .

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

Step 4.2.1.2

Multiply $7$ by $2$ .

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

Step 4.2.2

Find the common denominator.

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Step 4.2.2.1

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

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

Step 4.2.2.2

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

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

Step 4.2.2.3

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

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

Step 4.2.2.4

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

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

Step 4.2.2.5

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 4.2.2.6

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

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

Step 4.2.3

Combine the numerators over the common denominator.

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

Step 4.2.4

Simplify each term.

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Step 4.2.4.1

Multiply $28$ by $2$ .

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

Step 4.2.4.2

Multiply $14$ by $2$ .

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

Step 4.2.5

Simplify by adding and subtracting.

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Step 4.2.5.1

Subtract $7$ from $56$ .

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

Step 4.2.5.2

Add $49$ and $28$ .

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

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.

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

Step 5.2

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

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Cancel the common factor.

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

Step 5.2.1.1.2

Divide $7$ by $1$ .

$y = 28 - 1 \cdot 7 + 7 (3)$

Step 5.2.1.2

Multiply $- 1$ by $7$ .

$y = 28 - 7 + 7 (3)$

Step 5.2.1.3

Multiply $7$ by $3$ .

$y = 28 - 7 + 21$

Step 5.2.2

Simplify by adding and subtracting.

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Step 5.2.2.1

Subtract $7$ from $28$ .

$y = 21 + 21$

Step 5.2.2.2

Add $21$ and $21$ .

$y = 42$

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.

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