Algebra Examples

$2 y = 5 x + 11$

Step 1

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

$2 y = 5 (- 2) + 11$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify.

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Step 2.1.1

Multiply $5$ by $- 2$ .

$2 y = - 10 + 11$

Step 2.1.2

Add $- 10$ and $11$ .

$2 y = 1$

Step 2.2

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

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Step 2.2.1

Divide each term in $2 y = 1$ by $2$ .

$\frac{2 y}{2} = \frac{1}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{1}{2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{2}$

Step 3

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

$2 y = 5 (- 1) + 11$

Step 4

Solve the equation for $y$ .

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Step 4.1

Simplify.

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Step 4.1.1

Multiply $5$ by $- 1$ .

$2 y = - 5 + 11$

Step 4.1.2

Add $- 5$ and $11$ .

$2 y = 6$

Step 4.2

Divide each term in $2 y = 6$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 y = 6$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2}$

Step 4.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $6$ by $2$ .

$y = 3$

Step 5

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

$2 y = 5 (0) + 11$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify.

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Step 6.1.1

Multiply $5$ by $0$ .

$2 y = 0 + 11$

Step 6.1.2

Add $0$ and $11$ .

$2 y = 11$

Step 6.2

Divide each term in $2 y = 11$ by $2$ and simplify.

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Step 6.2.1

Divide each term in $2 y = 11$ by $2$ .

$\frac{2 y}{2} = \frac{11}{2}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $2$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{11}{2}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{11}{2}$

Step 7

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

$2 y = 5 (1) + 11$

Step 8

Solve the equation for $y$ .

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Step 8.1

Simplify.

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Step 8.1.1

Multiply $5$ by $1$ .

$2 y = 5 + 11$

Step 8.1.2

Add $5$ and $11$ .

$2 y = 16$

Step 8.2

Divide each term in $2 y = 16$ by $2$ and simplify.

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Step 8.2.1

Divide each term in $2 y = 16$ by $2$ .

$\frac{2 y}{2} = \frac{16}{2}$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Cancel the common factor of $2$ .

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Step 8.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{16}{2}$

Step 8.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{16}{2}$

Step 8.2.3

Simplify the right side.

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Step 8.2.3.1

Divide $16$ by $2$ .

$y = 8$

Step 9

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

$2 y = 5 (2) + 11$

Step 10

Solve the equation for $y$ .

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Step 10.1

Simplify.

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Step 10.1.1

Multiply $5$ by $2$ .

$2 y = 10 + 11$

Step 10.1.2

Add $10$ and $11$ .

$2 y = 21$

Step 10.2

Divide each term in $2 y = 21$ by $2$ and simplify.

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Step 10.2.1

Divide each term in $2 y = 21$ by $2$ .

$\frac{2 y}{2} = \frac{21}{2}$

Step 10.2.2

Simplify the left side.

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Step 10.2.2.1

Cancel the common factor of $2$ .

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Step 10.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{21}{2}$

Step 10.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{21}{2}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{1}{2} \\ - 1 & 3 \\ 0 & \frac{11}{2} \\ 1 & 8 \\ 2 & \frac{21}{2} \end{array}$

Step 12