Find Three Ordered Pair Solutions 7x+5y=-8

$7 x + 5 y = - 8$

Step 1

Solve the equation for $y$ .

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

$5 y = - 8 - 7 x$

Divide each term in $5 y = - 8 - 7 x$ by $5$ and simplify.

Divide each term in $5 y = - 8 - 7 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 8}{5} + \frac{- 7 x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 8}{5} + \frac{- 7 x}{5}$

Divide $y$ by $1$ .

$y = \frac{- 8}{5} + \frac{- 7 x}{5}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{8}{5} + \frac{- 7 x}{5}$

Move the negative in front of the fraction.

$y = - \frac{8}{5} - \frac{7 x}{5}$

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.

$y = - \frac{8}{5} - \frac{7 (0)}{5}$

Simplify $- \frac{8}{5} - \frac{7 (0)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 8 - 7 \cdot 0}{5}$

Simplify the expression.

Multiply $- 7$ by $0$ .

$y = \frac{- 8 + 0}{5}$

Add $- 8$ and $0$ .

$y = \frac{- 8}{5}$

Move the negative in front of the fraction.

$y = - \frac{8}{5}$

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

$(0, - \frac{8}{5})$

Step 4

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

Remove parentheses.

$y = - \frac{8}{5} - \frac{7 (1)}{5}$

Simplify $- \frac{8}{5} - \frac{7 (1)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 8 - 7 \cdot 1}{5}$

Simplify the expression.

Multiply $- 7$ by $1$ .

$y = \frac{- 8 - 7}{5}$

Subtract $7$ from $- 8$ .

$y = \frac{- 15}{5}$

Divide $- 15$ by $5$ .

$y = - 3$

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

$(1, - 3)$

Step 5

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

Remove parentheses.

$y = - \frac{8}{5} - \frac{7 (2)}{5}$

Simplify $- \frac{8}{5} - \frac{7 (2)}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 8 - 7 \cdot 2}{5}$

Simplify the expression.

Multiply $- 7$ by $2$ .

$y = \frac{- 8 - 14}{5}$

Subtract $14$ from $- 8$ .

$y = \frac{- 22}{5}$

Move the negative in front of the fraction.

$y = - \frac{22}{5}$

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

$(2, - \frac{22}{5})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{8}{5}), (1, - 3), (2, - \frac{22}{5})$

Step 7

Find Three Ordered Pair Solutions 7x+5y=-8

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