Find Three Ordered Pair Solutions 5x+7y=-3

$5 x + 7 y = - 3$

Step 1

Solve the equation for $y$ .

Subtract $5 x$ from both sides of the equation.

$7 y = - 3 - 5 x$

Divide each term in $7 y = - 3 - 5 x$ by $7$ and simplify.

Divide each term in $7 y = - 3 - 5 x$ by $7$ .

$\frac{7 y}{7} = \frac{- 3}{7} + \frac{- 5 x}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 3}{7} + \frac{- 5 x}{7}$

Divide $y$ by $1$ .

$y = \frac{- 3}{7} + \frac{- 5 x}{7}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{3}{7} + \frac{- 5 x}{7}$

Move the negative in front of the fraction.

$y = - \frac{3}{7} - \frac{5 x}{7}$

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.

$y = - \frac{3}{7} - \frac{5 (0)}{7}$

Simplify $- \frac{3}{7} - \frac{5 (0)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 - 5 \cdot 0}{7}$

Simplify the expression.

Multiply $- 5$ by $0$ .

$y = \frac{- 3 + 0}{7}$

Add $- 3$ and $0$ .

$y = \frac{- 3}{7}$

Move the negative in front of the fraction.

$y = - \frac{3}{7}$

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

$(0, - \frac{3}{7})$

Step 4

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

Remove parentheses.

$y = - \frac{3}{7} - \frac{5 (1)}{7}$

Simplify $- \frac{3}{7} - \frac{5 (1)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 - 5 \cdot 1}{7}$

Simplify the expression.

Multiply $- 5$ by $1$ .

$y = \frac{- 3 - 5}{7}$

Subtract $5$ from $- 3$ .

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

Move the negative in front of the fraction.

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

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

$(1, - \frac{8}{7})$

Step 5

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

Remove parentheses.

$y = - \frac{3}{7} - \frac{5 (2)}{7}$

Simplify $- \frac{3}{7} - \frac{5 (2)}{7}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 - 5 \cdot 2}{7}$

Simplify the expression.

Multiply $- 5$ by $2$ .

$y = \frac{- 3 - 10}{7}$

Subtract $10$ from $- 3$ .

$y = \frac{- 13}{7}$

Move the negative in front of the fraction.

$y = - \frac{13}{7}$

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

$(2, - \frac{13}{7})$

Step 6

These are three possible solutions to the equation.

$(0, - \frac{3}{7}), (1, - \frac{8}{7}), (2, - \frac{13}{7})$

Step 7

Find Three Ordered Pair Solutions 5x+7y=-3

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