Algebra Examples

$x + 5 y = - 5$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

Solve the equation for $y$ .

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Remove parentheses.

$- 2 + 5 y = - 5$

Move all terms not containing $y$ to the right side of the equation.

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Add $2$ to both sides of the equation.

$5 y = - 5 + 2$

Add $- 5$ and $2$ .

$5 y = - 3$

Divide each term in $5 y = - 3$ by $5$ and simplify.

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Divide each term in $5 y = - 3$ by $5$ .

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

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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Move the negative in front of the fraction.

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

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$(- 1) + 5 y = - 5$

Step 4

Solve the equation for $y$ .

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Remove parentheses.

$- 1 + 5 y = - 5$

Move all terms not containing $y$ to the right side of the equation.

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Add $1$ to both sides of the equation.

$5 y = - 5 + 1$

Add $- 5$ and $1$ .

$5 y = - 4$

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

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

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

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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Move the negative in front of the fraction.

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

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$(0) + 5 y = - 5$

Step 6

Solve the equation for $y$ .

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Add $0$ and $5 y$ .

$5 y = - 5$

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

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

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

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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Divide $- 5$ by $5$ .

$y = - 1$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$(1) + 5 y = - 5$

Step 8

Solve the equation for $y$ .

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Remove parentheses.

$1 + 5 y = - 5$

Move all terms not containing $y$ to the right side of the equation.

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Subtract $1$ from both sides of the equation.

$5 y = - 5 - 1$

Subtract $1$ from $- 5$ .

$5 y = - 6$

Divide each term in $5 y = - 6$ by $5$ and simplify.

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Divide each term in $5 y = - 6$ by $5$ .

$\frac{5 y}{5} = \frac{- 6}{5}$

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 y}{5} = \frac{- 6}{5}$

Divide $y$ by $1$ .

$y = \frac{- 6}{5}$

Simplify the right side.

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Move the negative in front of the fraction.

$y = - \frac{6}{5}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$(2) + 5 y = - 5$

Step 10

Solve the equation for $y$ .

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Remove parentheses.

$2 + 5 y = - 5$

Move all terms not containing $y$ to the right side of the equation.

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Subtract $2$ from both sides of the equation.

$5 y = - 5 - 2$

Subtract $2$ from $- 5$ .

$5 y = - 7$

Divide each term in $5 y = - 7$ by $5$ and simplify.

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Divide each term in $5 y = - 7$ by $5$ .

$\frac{5 y}{5} = \frac{- 7}{5}$

Simplify the left side.

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Cancel the common factor of $5$ .

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Cancel the common factor.

$\frac{5 y}{5} = \frac{- 7}{5}$

Divide $y$ by $1$ .

$y = \frac{- 7}{5}$

Simplify the right side.

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Move the negative in front of the fraction.

$y = - \frac{7}{5}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \frac{3}{5} \\ - 1 & - \frac{4}{5} \\ 0 & - 1 \\ 1 & - \frac{6}{5} \\ 2 & - \frac{7}{5} \end{array}$

Step 12