Finite Math Examples

$x = 2 y + 3$

Step 1

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

$- 2 = 2 y + 3$

Step 2

Solve the equation for $y$ .

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Step 2.1

Rewrite the equation as $2 y + 3 = - 2$ .

$2 y + 3 = - 2$

Step 2.2

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

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Step 2.2.1

Subtract $3$ from both sides of the equation.

$2 y = - 2 - 3$

Step 2.2.2

Subtract $3$ from $- 2$ .

$2 y = - 5$

Step 2.3

Divide each term in $2 y = - 5$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 y = - 5$ by $2$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

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

Step 3

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

$- 1 = 2 y + 3$

Step 4

Solve the equation for $y$ .

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Step 4.1

Rewrite the equation as $2 y + 3 = - 1$ .

$2 y + 3 = - 1$

Step 4.2

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

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$2 y = - 1 - 3$

Step 4.2.2

Subtract $3$ from $- 1$ .

$2 y = - 4$

Step 4.3

Divide each term in $2 y = - 4$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 y = - 4$ by $2$ .

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $y$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $- 4$ by $2$ .

$y = - 2$

Step 5

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

$0 = 2 y + 3$

Step 6

Solve the equation for $y$ .

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Step 6.1

Rewrite the equation as $2 y + 3 = 0$ .

$2 y + 3 = 0$

Step 6.2

Subtract $3$ from both sides of the equation.

$2 y = - 3$

Step 6.3

Divide each term in $2 y = - 3$ by $2$ and simplify.

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Step 6.3.1

Divide each term in $2 y = - 3$ by $2$ .

$\frac{2 y}{2} = \frac{- 3}{2}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $2$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 3}{2}$

Step 6.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3}{2}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Move the negative in front of the fraction.

$y = - \frac{3}{2}$

Step 7

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

$1 = 2 y + 3$

Step 8

Solve the equation for $y$ .

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Step 8.1

Rewrite the equation as $2 y + 3 = 1$ .

$2 y + 3 = 1$

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 $3$ from both sides of the equation.

$2 y = 1 - 3$

Step 8.2.2

Subtract $3$ from $1$ .

$2 y = - 2$

Step 8.3

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

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Step 8.3.1

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

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

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $2$ .

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Step 8.3.2.1.1

Cancel the common factor.

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

Step 8.3.2.1.2

Divide $y$ by $1$ .

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

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Divide $- 2$ by $2$ .

$y = - 1$

Step 9

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

$2 = 2 y + 3$

Step 10

Solve the equation for $y$ .

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Step 10.1

Rewrite the equation as $2 y + 3 = 2$ .

$2 y + 3 = 2$

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 $3$ from both sides of the equation.

$2 y = 2 - 3$

Step 10.2.2

Subtract $3$ from $2$ .

$2 y = - 1$

Step 10.3

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

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Step 10.3.1

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

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

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $2$ .

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Step 10.3.2.1.1

Cancel the common factor.

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

Step 10.3.2.1.2

Divide $y$ by $1$ .

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

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Move the negative in front of the fraction.

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

Step 11

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

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

Step 12