Algebra Examples

$5 x - 3 y = 15$

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

$5 (- 2) - 3 y = 15$

Solve the equation for $y$ .

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Multiply $5$ by $- 2$ .

$- 10 - 3 y = 15$

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

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Add $10$ to both sides of the equation.

$- 3 y = 15 + 10$

Add $15$ and $10$ .

$- 3 y = 25$

Divide each term in $- 3 y = 25$ by $- 3$ and simplify.

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Divide each term in $- 3 y = 25$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{25}{- 3}$

Simplify the left side.

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Cancel the common factor of $- 3$ .

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Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{25}{- 3}$

Divide $y$ by $1$ .

$y = \frac{25}{- 3}$

Simplify the right side.

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Move the negative in front of the fraction.

$y = - \frac{25}{3}$

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

$5 (- 1) - 3 y = 15$

Solve the equation for $y$ .

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Multiply $5$ by $- 1$ .

$- 5 - 3 y = 15$

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

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Add $5$ to both sides of the equation.

$- 3 y = 15 + 5$

Add $15$ and $5$ .

$- 3 y = 20$

Divide each term in $- 3 y = 20$ by $- 3$ and simplify.

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Divide each term in $- 3 y = 20$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{20}{- 3}$

Simplify the left side.

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Cancel the common factor of $- 3$ .

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Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{20}{- 3}$

Divide $y$ by $1$ .

$y = \frac{20}{- 3}$

Simplify the right side.

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Move the negative in front of the fraction.

$y = - \frac{20}{3}$

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

$5 (0) - 3 y = 15$

Solve the equation for $y$ .

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Simplify $5 (0) - 3 y$ .

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Multiply $5$ by $0$ .

$0 - 3 y = 15$

Subtract $3 y$ from $0$ .

$- 3 y = 15$

Divide each term in $- 3 y = 15$ by $- 3$ and simplify.

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Divide each term in $- 3 y = 15$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{15}{- 3}$

Simplify the left side.

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Cancel the common factor of $- 3$ .

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Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{15}{- 3}$

Divide $y$ by $1$ .

$y = \frac{15}{- 3}$

Simplify the right side.

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Divide $15$ by $- 3$ .

$y = - 5$

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

$5 (1) - 3 y = 15$

Solve the equation for $y$ .

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Multiply $5$ by $1$ .

$5 - 3 y = 15$

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

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Subtract $5$ from both sides of the equation.

$- 3 y = 15 - 5$

Subtract $5$ from $15$ .

$- 3 y = 10$

Divide each term in $- 3 y = 10$ by $- 3$ and simplify.

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Divide each term in $- 3 y = 10$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{10}{- 3}$

Simplify the left side.

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Cancel the common factor of $- 3$ .

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Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{10}{- 3}$

Divide $y$ by $1$ .

$y = \frac{10}{- 3}$

Simplify the right side.

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Move the negative in front of the fraction.

$y = - \frac{10}{3}$

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

$5 (2) - 3 y = 15$

Solve the equation for $y$ .

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Multiply $5$ by $2$ .

$10 - 3 y = 15$

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

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Subtract $10$ from both sides of the equation.

$- 3 y = 15 - 10$

Subtract $10$ from $15$ .

$- 3 y = 5$

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

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

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

Simplify the left side.

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Cancel the common factor of $- 3$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

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Move the negative in front of the fraction.

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

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

$\begin{array}{c} x & y \\ - 2 & - \frac{25}{3} \\ - 1 & - \frac{20}{3} \\ 0 & - 5 \\ 1 & - \frac{10}{3} \\ 2 & - \frac{5}{3} \end{array}$