Algebra Examples

$2 x = 12$ $x - 5 y = - 29$

Step 1

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

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Step 1.1

Divide each term in $2 x = 12$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2}$

$x - 5 y = - 29$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2}$

$x - 5 y = - 29$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{2}$

$x - 5 y = - 29$

$x = \frac{12}{2}$

$x - 5 y = - 29$

$x = \frac{12}{2}$

$x - 5 y = - 29$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $12$ by $2$ .

$x = 6$

$x - 5 y = - 29$

$x = 6$

$x - 5 y = - 29$

$x = 6$

$x - 5 y = - 29$

Step 2

Subtract $x$ from both sides of the equation.

$- 5 y = - 29 - x$

$x = 6$

Step 3

Divide each term in $- 5 y = - 29 - x$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 y = - 29 - x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 29}{- 5} + \frac{- x}{- 5}$

$x = 6$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 29}{- 5} + \frac{- x}{- 5}$

$x = 6$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 29}{- 5} + \frac{- x}{- 5}$

$x = 6$

$y = \frac{- 29}{- 5} + \frac{- x}{- 5}$

$x = 6$

$y = \frac{- 29}{- 5} + \frac{- x}{- 5}$

$x = 6$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{29}{5} + \frac{- x}{- 5}$

$x = 6$

Step 3.3.1.2

Dividing two negative values results in a positive value.

$y = \frac{29}{5} + \frac{x}{5}$

$x = 6$

$y = \frac{29}{5} + \frac{x}{5}$

$x = 6$

$y = \frac{29}{5} + \frac{x}{5}$

$x = 6$

$y = \frac{29}{5} + \frac{x}{5}$

$x = 6$

Step 4

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

$(6, 7)$

Step 5