Find Three Ordered Pair Solutions x=-6/7y

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

Step 1

Solve the equation for $y$ .

Rewrite the equation as $- \frac{6}{7} y = x$ .

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

Multiply both sides of the equation by $- \frac{7}{6}$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

Combine $y$ and $\frac{6}{7}$ .

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

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{7}{6}$ into the numerator.

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

Move the leading negative in $- \frac{y \cdot 6}{7}$ into the numerator.

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

Factor $7$ out of $- 7$ .

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

Cancel the common factor.

$\frac{7 \cdot - 1}{6} \cdot \frac{- y \cdot 6}{7} = - \frac{7}{6} x$

Rewrite the expression.

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

Cancel the common factor of $6$ .

Factor $6$ out of $- y \cdot 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{7}{6} x$

Multiply $y$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{7}{6} x$ .

Combine $x$ and $\frac{7}{6}$ .

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

Move $7$ to the left of $x$ .

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

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 x=-6/7y

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