Find Three Ordered Pair Solutions 6x+9y=0

$6 x + 9 y = 0$

Step 1

Solve the equation for $y$ .

Subtract $6 x$ from both sides of the equation.

$9 y = - 6 x$

Divide each term in $9 y = - 6 x$ by $9$ and simplify.

Divide each term in $9 y = - 6 x$ by $9$ .

$\frac{9 y}{9} = \frac{- 6 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 6 x}{9}$

Divide $y$ by $1$ .

$y = \frac{- 6 x}{9}$

Simplify the right side.

Cancel the common factor of $- 6$ and $9$ .

Factor $3$ out of $- 6 x$ .

$y = \frac{3 (- 2 x)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

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

Cancel the common factor.

$y = \frac{3 (- 2 x)}{3 \cdot 3}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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.

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

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

Cancel the common factor of $0$ and $3$ .

Factor $3$ out of $2 (0)$ .

$y = - \frac{3 (2 \cdot (0))}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = - \frac{3 (2 \cdot (0))}{3 (1)}$

Cancel the common factor.

$y = - \frac{3 (2 \cdot (0))}{3 \cdot 1}$

Rewrite the expression.

$y = - \frac{2 \cdot (0)}{1}$

Divide $2 \cdot (0)$ by $1$ .

$y = - (2 \cdot (0))$

Multiply $- (2 \cdot (0))$ .

Multiply $2$ by $0$ .

$y = - 0$

Multiply $- 1$ by $0$ .

$y = 0$

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

$(0, 0)$

Step 4

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

Remove parentheses.

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

Multiply $2$ by $1$ .

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

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.

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

Multiply $2$ by $2$ .

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

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.

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

Step 7

Find Three Ordered Pair Solutions 6x+9y=0

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