Finite Math Examples

$3 x + 4 y = 12$

Step 1

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

$3 (- 2) + 4 y = 12$

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $3$ by $- 2$ .

$- 6 + 4 y = 12$

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 $6$ to both sides of the equation.

$4 y = 12 + 6$

Step 2.2.2

Add $12$ and $6$ .

$4 y = 18$

Step 2.3

Divide each term in $4 y = 18$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 y = 18$ by $4$ .

$\frac{4 y}{4} = \frac{18}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{18}{4}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Cancel the common factor of $18$ and $4$ .

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Step 2.3.3.1.1

Factor $2$ out of $18$ .

$y = \frac{2 (9)}{4}$

Step 2.3.3.1.2

Cancel the common factors.

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Step 2.3.3.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 9}{2 \cdot 2}$

Step 2.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 9}{2 \cdot 2}$

Step 2.3.3.1.2.3

Rewrite the expression.

$y = \frac{9}{2}$

Step 3

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

$3 (- 1) + 4 y = 12$

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $3$ by $- 1$ .

$- 3 + 4 y = 12$

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 $3$ to both sides of the equation.

$4 y = 12 + 3$

Step 4.2.2

Add $12$ and $3$ .

$4 y = 15$

Step 4.3

Divide each term in $4 y = 15$ by $4$ and simplify.

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Step 4.3.1

Divide each term in $4 y = 15$ by $4$ .

$\frac{4 y}{4} = \frac{15}{4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{15}{4}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{15}{4}$

Step 5

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

$3 (0) + 4 y = 12$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $3 (0) + 4 y$ .

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Step 6.1.1

Multiply $3$ by $0$ .

$0 + 4 y = 12$

Step 6.1.2

Add $0$ and $4 y$ .

$4 y = 12$

Step 6.2

Divide each term in $4 y = 12$ by $4$ and simplify.

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Step 6.2.1

Divide each term in $4 y = 12$ by $4$ .

$\frac{4 y}{4} = \frac{12}{4}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $4$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{12}{4}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{4}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $12$ by $4$ .

$y = 3$

Step 7

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

$3 (1) + 4 y = 12$

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $3$ by $1$ .

$3 + 4 y = 12$

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.

$4 y = 12 - 3$

Step 8.2.2

Subtract $3$ from $12$ .

$4 y = 9$

Step 8.3

Divide each term in $4 y = 9$ by $4$ and simplify.

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Step 8.3.1

Divide each term in $4 y = 9$ by $4$ .

$\frac{4 y}{4} = \frac{9}{4}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $4$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{9}{4}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{4}$

Step 9

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

$3 (2) + 4 y = 12$

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $3$ by $2$ .

$6 + 4 y = 12$

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 $6$ from both sides of the equation.

$4 y = 12 - 6$

Step 10.2.2

Subtract $6$ from $12$ .

$4 y = 6$

Step 10.3

Divide each term in $4 y = 6$ by $4$ and simplify.

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Step 10.3.1

Divide each term in $4 y = 6$ by $4$ .

$\frac{4 y}{4} = \frac{6}{4}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $4$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{6}{4}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{4}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Cancel the common factor of $6$ and $4$ .

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Step 10.3.3.1.1

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{4}$

Step 10.3.3.1.2

Cancel the common factors.

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Step 10.3.3.1.2.1

Factor $2$ out of $4$ .

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

Step 10.3.3.1.2.2

Cancel the common factor.

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

Step 10.3.3.1.2.3

Rewrite the expression.

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

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{9}{2} \\ - 1 & \frac{15}{4} \\ 0 & 3 \\ 1 & \frac{9}{4} \\ 2 & \frac{3}{2} \end{array}$

Step 12