Find Three Ordered Pair Solutions 7x+8y=56

$7 x + 8 y = 56$

Step 1

Solve the equation for $y$ .

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

$8 y = 56 - 7 x$

Divide each term in $8 y = 56 - 7 x$ by $8$ and simplify.

Divide each term in $8 y = 56 - 7 x$ by $8$ .

$\frac{8 y}{8} = \frac{56}{8} + \frac{- 7 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{56}{8} + \frac{- 7 x}{8}$

Divide $y$ by $1$ .

$y = \frac{56}{8} + \frac{- 7 x}{8}$

Simplify the right side.

Simplify each term.

Divide $56$ by $8$ .

$y = 7 + \frac{- 7 x}{8}$

Move the negative in front of the fraction.

$y = 7 - \frac{7 x}{8}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 7 - \frac{7 (0)}{8}$

Simplify $7 - \frac{7 (0)}{8}$ .

Simplify each term.

Cancel the common factor of $0$ and $8$ .

Factor $8$ out of $7 (0)$ .

$y = 7 - \frac{8 (7 \cdot (0))}{8}$

Cancel the common factors.

Factor $8$ out of $8$ .

$y = 7 - \frac{8 (7 \cdot (0))}{8 (1)}$

Cancel the common factor.

$y = 7 - \frac{8 (7 \cdot (0))}{8 \cdot 1}$

Rewrite the expression.

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

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

$y = 7 - (7 \cdot (0))$

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

Multiply $7$ by $0$ .

$y = 7 - 0$

Multiply $- 1$ by $0$ .

$y = 7 + 0$

Add $7$ and $0$ .

$y = 7$

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

$(0, 7)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 7 - \frac{7 (1)}{8}$

Simplify $7 - \frac{7 (1)}{8}$ .

Multiply $7$ by $1$ .

$y = 7 - \frac{7}{8}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = 7 \cdot \frac{8}{8} - \frac{7}{8}$

Combine $7$ and $\frac{8}{8}$ .

$y = \frac{7 \cdot 8}{8} - \frac{7}{8}$

Combine the numerators over the common denominator.

$y = \frac{7 \cdot 8 - 7}{8}$

Simplify the numerator.

Multiply $7$ by $8$ .

$y = \frac{56 - 7}{8}$

Subtract $7$ from $56$ .

$y = \frac{49}{8}$

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

$(1, \frac{49}{8})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = 7 - \frac{7 (2)}{8}$

Simplify $7 - \frac{7 (2)}{8}$ .

Cancel the common factor of $2$ and $8$ .

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

$y = 7 - \frac{2 \cdot 7}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$y = 7 - \frac{2 \cdot 7}{2 \cdot 4}$

Cancel the common factor.

$y = 7 - \frac{2 \cdot 7}{2 \cdot 4}$

Rewrite the expression.

$y = 7 - \frac{7}{4}$

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = 7 \cdot \frac{4}{4} - \frac{7}{4}$

Combine $7$ and $\frac{4}{4}$ .

$y = \frac{7 \cdot 4}{4} - \frac{7}{4}$

Combine the numerators over the common denominator.

$y = \frac{7 \cdot 4 - 7}{4}$

Simplify the numerator.

Multiply $7$ by $4$ .

$y = \frac{28 - 7}{4}$

Subtract $7$ from $28$ .

$y = \frac{21}{4}$

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

$(2, \frac{21}{4})$

Step 6

These are three possible solutions to the equation.

$(0, 7), (1, \frac{49}{8}), (2, \frac{21}{4})$

Step 7

Find Three Ordered Pair Solutions 7x+8y=56

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