Find Three Ordered Pair Solutions -6x-5y=30

$- 6 x - 5 y = 30$

Step 1

Solve the equation for $y$ .

Add $6 x$ to both sides of the equation.

$- 5 y = 30 + 6 x$

Divide each term in $- 5 y = 30 + 6 x$ by $- 5$ and simplify.

Divide each term in $- 5 y = 30 + 6 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{30}{- 5} + \frac{6 x}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{30}{- 5} + \frac{6 x}{- 5}$

Divide $y$ by $1$ .

$y = \frac{30}{- 5} + \frac{6 x}{- 5}$

Simplify the right side.

Simplify each term.

Divide $30$ by $- 5$ .

$y = - 6 + \frac{6 x}{- 5}$

Move the negative in front of the fraction.

$y = - 6 - \frac{6 x}{5}$

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.

$y = - 6 - \frac{6 (0)}{5}$

Simplify $- 6 - \frac{6 (0)}{5}$ .

Simplify each term.

Cancel the common factor of $0$ and $5$ .

Factor $5$ out of $6 (0)$ .

$y = - 6 - \frac{5 (6 \cdot (0))}{5}$

Cancel the common factors.

Factor $5$ out of $5$ .

$y = - 6 - \frac{5 (6 \cdot (0))}{5 (1)}$

Cancel the common factor.

$y = - 6 - \frac{5 (6 \cdot (0))}{5 \cdot 1}$

Rewrite the expression.

$y = - 6 - \frac{6 \cdot (0)}{1}$

Divide $6 \cdot (0)$ by $1$ .

$y = - 6 - (6 \cdot (0))$

Multiply $- (6 \cdot (0))$ .

Multiply $6$ by $0$ .

$y = - 6 - 0$

Multiply $- 1$ by $0$ .

$y = - 6 + 0$

Add $- 6$ and $0$ .

$y = - 6$

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

$(0, - 6)$

Step 4

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

Remove parentheses.

$y = - 6 - \frac{6 (1)}{5}$

Simplify $- 6 - \frac{6 (1)}{5}$ .

Multiply $6$ by $1$ .

$y = - 6 - \frac{6}{5}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - 6 \cdot \frac{5}{5} - \frac{6}{5}$

Combine $- 6$ and $\frac{5}{5}$ .

$y = \frac{- 6 \cdot 5}{5} - \frac{6}{5}$

Combine the numerators over the common denominator.

$y = \frac{- 6 \cdot 5 - 6}{5}$

Simplify the numerator.

Multiply $- 6$ by $5$ .

$y = \frac{- 30 - 6}{5}$

Subtract $6$ from $- 30$ .

$y = \frac{- 36}{5}$

Move the negative in front of the fraction.

$y = - \frac{36}{5}$

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

$(1, - \frac{36}{5})$

Step 5

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

Remove parentheses.

$y = - 6 - \frac{6 (2)}{5}$

Simplify $- 6 - \frac{6 (2)}{5}$ .

Multiply $6$ by $2$ .

$y = - 6 - \frac{12}{5}$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = - 6 \cdot \frac{5}{5} - \frac{12}{5}$

Combine $- 6$ and $\frac{5}{5}$ .

$y = \frac{- 6 \cdot 5}{5} - \frac{12}{5}$

Combine the numerators over the common denominator.

$y = \frac{- 6 \cdot 5 - 12}{5}$

Simplify the numerator.

Multiply $- 6$ by $5$ .

$y = \frac{- 30 - 12}{5}$

Subtract $12$ from $- 30$ .

$y = \frac{- 42}{5}$

Move the negative in front of the fraction.

$y = - \frac{42}{5}$

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

$(2, - \frac{42}{5})$

Step 6

These are three possible solutions to the equation.

$(0, - 6), (1, - \frac{36}{5}), (2, - \frac{42}{5})$

Step 7

Find Three Ordered Pair Solutions -6x-5y=30

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