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

$7 x - 5 y = - 3$

Step 1

Solve the equation for $y$ .

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

$- 5 y = - 3 - 7 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

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

Dividing two negative values results in a positive value.

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

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.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $7$ by $0$ .

$y = \frac{3 + 0}{5}$

Add $3$ and $0$ .

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

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

$(0, \frac{3}{5})$

Step 4

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $7$ by $1$ .

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

Add $3$ and $7$ .

$y = \frac{10}{5}$

Divide $10$ by $5$ .

$y = 2$

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

$(1, 2)$

Step 5

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

Remove parentheses.

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

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

Combine the numerators over the common denominator.

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

Simplify the expression.

Multiply $7$ by $2$ .

$y = \frac{3 + 14}{5}$

Add $3$ and $14$ .

$y = \frac{17}{5}$

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

$(2, \frac{17}{5})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{3}{5}), (1, 2), (2, \frac{17}{5})$

Step 7

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

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