Algebra Examples

$- 4 x - 5 y = 11$ $2 x - y = 5$

Step 1

Add $4 x$ to both sides of the equation.

$- 5 y = 11 + 4 x$

$2 x - y = 5$

Step 2

Divide each term in $- 5 y = 11 + 4 x$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 y = 11 + 4 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{11}{- 5} + \frac{4 x}{- 5}$

$2 x - y = 5$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{11}{- 5} + \frac{4 x}{- 5}$

$2 x - y = 5$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{11}{- 5} + \frac{4 x}{- 5}$

$2 x - y = 5$

$y = \frac{11}{- 5} + \frac{4 x}{- 5}$

$2 x - y = 5$

$y = \frac{11}{- 5} + \frac{4 x}{- 5}$

$2 x - y = 5$

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.

$y = - \frac{11}{5} + \frac{4 x}{- 5}$

$2 x - y = 5$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{11}{5} - \frac{4 x}{5}$

$2 x - y = 5$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$2 x - y = 5$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$2 x - y = 5$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$2 x - y = 5$

Step 3

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

$- y = 5 - 2 x$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 4

Divide each term in $- y = 5 - 2 x$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- y = 5 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 4.2.2

Divide $y$ by $1$ .

$y = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$y = \frac{5}{- 1} + \frac{- 2 x}{- 1}$

$y = - \frac{11}{5} - \frac{4 x}{5}$

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

Divide $5$ by $- 1$ .

$y = - 5 + \frac{- 2 x}{- 1}$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 4.3.1.2

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y = - 5 - 1 \cdot (- 2 x)$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 4.3.1.3

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = - 5 - (- 2 x)$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 4.3.1.4

Multiply $- 2$ by $- 1$ .

$y = - 5 + 2 x$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$y = - 5 + 2 x$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$y = - 5 + 2 x$

$y = - \frac{11}{5} - \frac{4 x}{5}$

$y = - 5 + 2 x$

$y = - \frac{11}{5} - \frac{4 x}{5}$

Step 5

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

$(1, - 3)$

Step 6