Find Three Ordered Pair Solutions 7x+6y=0

$7 x + 6 y = 0$

Step 1

Solve the equation for $y$ .

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

$6 y = - 7 x$

Divide each term in $6 y = - 7 x$ by $6$ and simplify.

Divide each term in $6 y = - 7 x$ by $6$ .

$\frac{6 y}{6} = \frac{- 7 x}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 7 x}{6}$

Divide $y$ by $1$ .

$y = \frac{- 7 x}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{7 x}{6}$

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.

$y = - \frac{7 (0)}{6}$

Simplify $- \frac{7 (0)}{6}$ .

Cancel the common factor of $0$ and $6$ .

Factor $6$ out of $7 (0)$ .

$y = - \frac{6 (7 \cdot (0))}{6}$

Cancel the common factors.

Factor $6$ out of $6$ .

$y = - \frac{6 (7 \cdot (0))}{6 (1)}$

Cancel the common factor.

$y = - \frac{6 (7 \cdot (0))}{6 \cdot 1}$

Rewrite the expression.

$y = - \frac{7 \cdot (0)}{1}$

Divide $7 \cdot (0)$ by $1$ .

$y = - (7 \cdot (0))$

Multiply $- (7 \cdot (0))$ .

Multiply $7$ 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.

$y = - \frac{7 (1)}{6}$

Multiply $7$ by $1$ .

$y = - \frac{7}{6}$

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

$(1, - \frac{7}{6})$

Step 5

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

Remove parentheses.

$y = - \frac{7 (2)}{6}$

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $7 (2)$ .

$y = - \frac{2 \cdot 7}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 6

These are three possible solutions to the equation.

$(0, 0), (1, - \frac{7}{6}), (2, - \frac{7}{3})$

Step 7

Find Three Ordered Pair Solutions 7x+6y=0

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