Algebra Examples

$2 x - 3 y = - 12$ $y = - \frac{5}{3} x - 3$

Step 1

Subtract $2 x$ from both sides of the equation.

$- 3 y = - 12 - 2 x$

$y = - \frac{5}{3} x - 3$

Step 2

Divide each term in $- 3 y = - 12 - 2 x$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 y = - 12 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 12}{- 3} + \frac{- 2 x}{- 3}$

$y = - \frac{5}{3} x - 3$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 12}{- 3} + \frac{- 2 x}{- 3}$

$y = - \frac{5}{3} x - 3$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 3} + \frac{- 2 x}{- 3}$

$y = - \frac{5}{3} x - 3$

$y = \frac{- 12}{- 3} + \frac{- 2 x}{- 3}$

$y = - \frac{5}{3} x - 3$

$y = \frac{- 12}{- 3} + \frac{- 2 x}{- 3}$

$y = - \frac{5}{3} x - 3$

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 $- 12$ by $- 3$ .

$y = 4 + \frac{- 2 x}{- 3}$

$y = - \frac{5}{3} x - 3$

Step 2.3.1.2

Dividing two negative values results in a positive value.

$y = 4 + \frac{2 x}{3}$

$y = - \frac{5}{3} x - 3$

$y = 4 + \frac{2 x}{3}$

$y = - \frac{5}{3} x - 3$

$y = 4 + \frac{2 x}{3}$

$y = - \frac{5}{3} x - 3$

$y = 4 + \frac{2 x}{3}$

$y = - \frac{5}{3} x - 3$

Step 3

Simplify each term.

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Step 3.1

Combine $x$ and $\frac{5}{3}$ .

$y = - \frac{x \cdot 5}{3} - 3$

$y = 4 + \frac{2 x}{3}$

Step 3.2

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{3} - 3$

$y = 4 + \frac{2 x}{3}$

$y = - \frac{5 x}{3} - 3$

$y = 4 + \frac{2 x}{3}$

Step 4

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

$(- 3, 2)$

Step 5