Algebra Examples

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

Step 1

Solve the equation for $y$ .

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Step 1.1

Rewrite the equation as $- \frac{1}{6} y = x$ .

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

Step 1.2

Multiply both sides of the equation by $- 6$ .

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

Step 1.3

Simplify the left side.

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Step 1.3.1

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

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Step 1.3.1.1

Combine $y$ and $\frac{1}{6}$ .

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

Step 1.3.1.2

Cancel the common factor of $6$ .

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Step 1.3.1.2.1

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

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

Step 1.3.1.2.2

Factor $6$ out of $- 6$ .

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

Step 1.3.1.2.3

Cancel the common factor.

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

Step 1.3.1.2.4

Rewrite the expression.

$- - y = - 6 x$

Step 1.3.1.3

Multiply.

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Step 1.3.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - 6 x$

Step 1.3.1.3.2

Multiply $y$ by $1$ .

$y = - 6 x$

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.

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Step 3.1

Remove parentheses.

$y = - 6 \cdot 0$

Step 3.2

Multiply $- 6$ by $0$ .

$y = 0$

Step 3.3

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.

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Step 4.1

Remove parentheses.

$y = - 6 \cdot 1$

Step 4.2

Multiply $- 6$ by $1$ .

$y = - 6$

Step 4.3

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

$(1, - 6)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = - 6 \cdot 2$

Step 5.2

Multiply $- 6$ by $2$ .

$y = - 12$

Step 5.3

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

$(2, - 12)$

Step 6

These are three possible solutions to the equation.

$(0, 0), (1, - 6), (2, - 12)$

Step 7