Algebra Examples

$6 x - y = 9$ , $\frac{1}{3} y = - 3 + 2 x$

Step 1

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

$- y = 9 - 6 x$

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

Step 2

Divide each term in $- y = 9 - 6 x$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- y = 9 - 6 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{9}{- 1} + \frac{- 6 x}{- 1}$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{9}{- 1} + \frac{- 6 x}{- 1}$

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

Step 2.2.2

Divide $y$ by $1$ .

$y = \frac{9}{- 1} + \frac{- 6 x}{- 1}$

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

$y = \frac{9}{- 1} + \frac{- 6 x}{- 1}$

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $9$ by $- 1$ .

$y = - 9 + \frac{- 6 x}{- 1}$

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

Step 2.3.1.2

Move the negative one from the denominator of $\frac{- 6 x}{- 1}$ .

$y = - 9 - 1 \cdot (- 6 x)$

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

Step 2.3.1.3

Rewrite $- 1 \cdot (- 6 x)$ as $- (- 6 x)$ .

$y = - 9 - (- 6 x)$

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

Step 2.3.1.4

Multiply $- 6$ by $- 1$ .

$y = - 9 + 6 x$

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

$y = - 9 + 6 x$

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

$y = - 9 + 6 x$

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

$y = - 9 + 6 x$

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

Step 3

Multiply both sides of the equation by $3$ .

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

$y = - 9 + 6 x$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $3 (\frac{1}{3} y)$ .

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Step 4.1.1.1

Combine $\frac{1}{3}$ and $y$ .

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

$y = - 9 + 6 x$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Cancel the common factor.

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

$y = - 9 + 6 x$

Step 4.1.1.2.2

Rewrite the expression.

$y = 3 (- 3 + 2 x)$

$y = - 9 + 6 x$

$y = 3 (- 3 + 2 x)$

$y = - 9 + 6 x$

$y = 3 (- 3 + 2 x)$

$y = - 9 + 6 x$

$y = 3 (- 3 + 2 x)$

$y = - 9 + 6 x$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $3 (- 3 + 2 x)$ .

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Step 4.2.1.1

Apply the distributive property.

$y = 3 \cdot - 3 + 3 (2 x)$

$y = - 9 + 6 x$

Step 4.2.1.2

Multiply.

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Step 4.2.1.2.1

Multiply $3$ by $- 3$ .

$y = - 9 + 3 (2 x)$

$y = - 9 + 6 x$

Step 4.2.1.2.2

Multiply $2$ by $3$ .

$y = - 9 + 6 x$

Step 5

Reorder $- 9$ and $6 x$ .

$y = 6 x - 9$

$y = - 9 + 6 x$

Step 6

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

Always true

Step 7