Algebra Examples

$x + 5 y = 5$ $y = - \frac{4}{5} x - 2$

Step 1

Subtract $x$ from both sides of the equation.

$5 y = 5 - x$

$y = - \frac{4}{5} x - 2$

Step 2

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

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Step 2.1

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

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

$y = - \frac{4}{5} x - 2$

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.

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

$y = - \frac{4}{5} x - 2$

Step 2.2.1.2

Divide $y$ by $1$ .

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

$y = - \frac{4}{5} x - 2$

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

$y = - \frac{4}{5} x - 2$

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

$y = - \frac{4}{5} x - 2$

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 $5$ by $5$ .

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

$y = - \frac{4}{5} x - 2$

Step 2.3.1.2

Move the negative in front of the fraction.

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

$y = - \frac{4}{5} x - 2$

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

$y = - \frac{4}{5} x - 2$

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

$y = - \frac{4}{5} x - 2$

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

$y = - \frac{4}{5} x - 2$

Step 3

Simplify each term.

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Step 3.1

Combine $x$ and $\frac{4}{5}$ .

$y = - \frac{x \cdot 4}{5} - 2$

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

Step 3.2

Move $4$ to the left of $x$ .

$y = - \frac{4 x}{5} - 2$

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

$y = - \frac{4 x}{5} - 2$

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

Step 4

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

$(- 5, 2)$

Step 5