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

$- 5 x - 3 y = - 7$

Step 1

Solve the equation for $y$ .

Add $5 x$ to both sides of the equation.

$- 3 y = - 7 + 5 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Move the negative in front of the fraction.

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $- 5$ by $0$ .

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

Add $7$ and $0$ .

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

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

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

Step 4

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $- 5$ by $1$ .

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

Subtract $5$ from $7$ .

$y = \frac{2}{3}$

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

$(1, \frac{2}{3})$

Step 5

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $- 5$ by $2$ .

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

Subtract $10$ from $7$ .

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

Divide $- 3$ by $3$ .

$y = - 1$

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

$(2, - 1)$

Step 6

These are three possible solutions to the equation.

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

Step 7

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

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