Pre-Algebra Examples

$x + 5 y = 10$

Step 1

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

$(- 2) + 5 y = 10$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$- 2 + 5 y = 10$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the equation.

$5 y = 10 + 2$

Step 2.2.2

Add $10$ and $2$ .

$5 y = 12$

Step 2.3

Divide each term in $5 y = 12$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 y = 12$ by $5$ .

$\frac{5 y}{5} = \frac{12}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{12}{5}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{5}$

Step 3

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

$(- 1) + 5 y = 10$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$- 1 + 5 y = 10$

Step 4.2

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

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Step 4.2.1

Add $1$ to both sides of the equation.

$5 y = 10 + 1$

Step 4.2.2

Add $10$ and $1$ .

$5 y = 11$

Step 4.3

Divide each term in $5 y = 11$ by $5$ and simplify.

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Step 4.3.1

Divide each term in $5 y = 11$ by $5$ .

$\frac{5 y}{5} = \frac{11}{5}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $5$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{11}{5}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{11}{5}$

Step 5

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

$(0) + 5 y = 10$

Step 6

Solve the equation for $y$ .

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Step 6.1

Add $0$ and $5 y$ .

$5 y = 10$

Step 6.2

Divide each term in $5 y = 10$ by $5$ and simplify.

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Step 6.2.1

Divide each term in $5 y = 10$ by $5$ .

$\frac{5 y}{5} = \frac{10}{5}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $5$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{10}{5}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{10}{5}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $10$ by $5$ .

$y = 2$

Step 7

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

$(1) + 5 y = 10$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$1 + 5 y = 10$

Step 8.2

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

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Step 8.2.1

Subtract $1$ from both sides of the equation.

$5 y = 10 - 1$

Step 8.2.2

Subtract $1$ from $10$ .

$5 y = 9$

Step 8.3

Divide each term in $5 y = 9$ by $5$ and simplify.

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Step 8.3.1

Divide each term in $5 y = 9$ by $5$ .

$\frac{5 y}{5} = \frac{9}{5}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $5$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{9}{5}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{5}$

Step 9

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

$(2) + 5 y = 10$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$2 + 5 y = 10$

Step 10.2

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

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Step 10.2.1

Subtract $2$ from both sides of the equation.

$5 y = 10 - 2$

Step 10.2.2

Subtract $2$ from $10$ .

$5 y = 8$

Step 10.3

Divide each term in $5 y = 8$ by $5$ and simplify.

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Step 10.3.1

Divide each term in $5 y = 8$ by $5$ .

$\frac{5 y}{5} = \frac{8}{5}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $5$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{8}{5}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{5}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{12}{5} \\ - 1 & \frac{11}{5} \\ 0 & 2 \\ 1 & \frac{9}{5} \\ 2 & \frac{8}{5} \end{array}$

Step 12