Find Three Ordered Pair Solutions 7x+2y-14z=56

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

Step 1

Solve the equation for $y$ .

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

Subtract $7 x$ from both sides of the equation.

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $56$ by $2$ .

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

Move the negative in front of the fraction.

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

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

Factor $2$ out of $14 z$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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 $z$ .

Remove parentheses.

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

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

Simplify each term.

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

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Multiply $7$ by $0$ .

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

Multiply $- 1$ by $0$ .

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

Multiply $7$ by $1$ .

$y = 28 + 0 + 7$

Simplify by adding numbers.

Add $28$ and $0$ .

$y = 28 + 7$

Add $28$ and $7$ .

$y = 35$

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 $z$ .

Remove parentheses.

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

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

Simplify each term.

Multiply $7$ by $1$ .

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

Multiply $7$ by $2$ .

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

Find the common denominator.

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

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $28$ by $2$ .

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

Multiply $14$ by $2$ .

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

Simplify by adding and subtracting.

Subtract $7$ from $56$ .

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

Add $49$ and $28$ .

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

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 $z$ .

Remove parentheses.

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

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

Simplify each term.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $7$ by $1$ .

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

Multiply $- 1$ by $7$ .

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

Multiply $7$ by $3$ .

$y = 28 - 7 + 21$

Simplify by adding and subtracting.

Subtract $7$ from $28$ .

$y = 21 + 21$

Add $21$ and $21$ .

$y = 42$

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.

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

Find Three Ordered Pair Solutions 7x+2y-14z=56

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