Find Three Ordered Pair Solutions -x-3y=-6

$- x - 3 y = - 6$

Step 1

Solve the equation for $y$ .

Add $x$ to both sides of the equation.

$- 3 y = - 6 + x$

Divide each term in $- 3 y = - 6 + x$ by $- 3$ and simplify.

Divide each term in $- 3 y = - 6 + x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3} + \frac{x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 6}{- 3} + \frac{x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 3} + \frac{x}{- 3}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 3$ .

$y = 2 + \frac{x}{- 3}$

Move the negative in front of the fraction.

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

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.

$y = 2 - \frac{0}{3}$

Simplify $2 - \frac{0}{3}$ .

Simplify each term.

Divide $0$ by $3$ .

$y = 2 - 0$

Multiply $- 1$ by $0$ .

$y = 2 + 0$

Add $2$ and $0$ .

$y = 2$

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

$(0, 2)$

Step 4

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

Remove parentheses.

$y = 2 - \frac{1}{3}$

Simplify $2 - \frac{1}{3}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 2 \cdot \frac{3}{3} - \frac{1}{3}$

Combine $2$ and $\frac{3}{3}$ .

$y = \frac{2 \cdot 3}{3} - \frac{1}{3}$

Combine the numerators over the common denominator.

$y = \frac{2 \cdot 3 - 1}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$y = \frac{6 - 1}{3}$

Subtract $1$ from $6$ .

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

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

$(1, \frac{5}{3})$

Step 5

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

Remove parentheses.

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

Simplify $2 - \frac{2}{3}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $2$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

$y = \frac{6 - 2}{3}$

Subtract $2$ from $6$ .

$y = \frac{4}{3}$

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

$(2, \frac{4}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, \frac{5}{3}), (2, \frac{4}{3})$

Step 7

Find Three Ordered Pair Solutions -x-3y=-6

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