Algebra Examples

$x + 2 y = - 13$ , $12 x + 5 y = - 4$

Step 1

Subtract $x$ from both sides of the equation.

$2 y = - 13 - x$

$12 x + 5 y = - 4$

Step 2

Divide each term in $2 y = - 13 - x$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 y = - 13 - x$ by $2$ .

$\frac{2 y}{2} = \frac{- 13}{2} + \frac{- x}{2}$

$12 x + 5 y = - 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 13}{2} + \frac{- x}{2}$

$12 x + 5 y = - 4$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 13}{2} + \frac{- x}{2}$

$12 x + 5 y = - 4$

$y = \frac{- 13}{2} + \frac{- x}{2}$

$12 x + 5 y = - 4$

$y = \frac{- 13}{2} + \frac{- x}{2}$

$12 x + 5 y = - 4$

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

Move the negative in front of the fraction.

$y = - \frac{13}{2} + \frac{- x}{2}$

$12 x + 5 y = - 4$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{13}{2} - \frac{x}{2}$

$12 x + 5 y = - 4$

$y = - \frac{13}{2} - \frac{x}{2}$

$12 x + 5 y = - 4$

$y = - \frac{13}{2} - \frac{x}{2}$

$12 x + 5 y = - 4$

$y = - \frac{13}{2} - \frac{x}{2}$

$12 x + 5 y = - 4$

Step 3

Subtract $12 x$ from both sides of the equation.

$5 y = - 4 - 12 x$

$y = - \frac{13}{2} - \frac{x}{2}$

Step 4

Divide each term in $5 y = - 4 - 12 x$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 y = - 4 - 12 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 4}{5} + \frac{- 12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 4}{5} + \frac{- 12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4}{5} + \frac{- 12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

$y = \frac{- 4}{5} + \frac{- 12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

$y = \frac{- 4}{5} + \frac{- 12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative in front of the fraction.

$y = - \frac{4}{5} + \frac{- 12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

Step 4.3.1.2

Move the negative in front of the fraction.

$y = - \frac{4}{5} - \frac{12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

$y = - \frac{4}{5} - \frac{12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

$y = - \frac{4}{5} - \frac{12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

$y = - \frac{4}{5} - \frac{12 x}{5}$

$y = - \frac{13}{2} - \frac{x}{2}$

Step 5

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

$(3, - 8)$

Step 6