Finite Math Examples

3 x - 2 y = - 5

$3 x - 2 y = - 5$ ,

x + 2 y - 9

$x + 2 y - 9$

Step 1

Add

2 y

$2 y$ to both sides of the equation.

3 x = - 5 + 2 y

$3 x = - 5 + 2 y$

Step 2

Divide each term in

3 x = - 5 + 2 y

$3 x = - 5 + 2 y$ by

3

$3$ and simplify.

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Step 2.1

Divide each term in

3 x = - 5 + 2 y

$3 x = - 5 + 2 y$ by

3

$3$ .

\frac{3 x}{3} = \frac{- 5}{3} + \frac{2 y}{3}

$\frac{3 x}{3} = \frac{- 5}{3} + \frac{2 y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

3

$3$ .

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Step 2.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{- 5}{3} + \frac{2 y}{3}

$\frac{3 x}{3} = \frac{- 5}{3} + \frac{2 y}{3}$

Step 2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 5}{3} + \frac{2 y}{3}

$x = \frac{- 5}{3} + \frac{2 y}{3}$

x = \frac{- 5}{3} + \frac{2 y}{3}

$x = \frac{- 5}{3} + \frac{2 y}{3}$

x = \frac{- 5}{3} + \frac{2 y}{3}

$x = \frac{- 5}{3} + \frac{2 y}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

x = - \frac{5}{3} + \frac{2 y}{3}

$x = - \frac{5}{3} + \frac{2 y}{3}$

x = - \frac{5}{3} + \frac{2 y}{3}

$x = - \frac{5}{3} + \frac{2 y}{3}$

x = - \frac{5}{3} + \frac{2 y}{3}

$x = - \frac{5}{3} + \frac{2 y}{3}$

Step 3

Replace the variable

x

$x$ with

- \frac{5}{3} + \frac{2 y}{3}

$- \frac{5}{3} + \frac{2 y}{3}$ in the expression.

(- \frac{5}{3} + \frac{2 y}{3}) + 2 y - 9

$(- \frac{5}{3} + \frac{2 y}{3}) + 2 y - 9$

Step 4

To write

- 9

$- 9$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

(\frac{2 y}{3}) + 2 y - \frac{5}{3} - 9 \cdot \frac{3}{3}

$(\frac{2 y}{3}) + 2 y - \frac{5}{3} - 9 \cdot \frac{3}{3}$

Step 5

Combine

- 9

$- 9$ and

\frac{3}{3}

$\frac{3}{3}$ .

(\frac{2 y}{3}) + 2 y - \frac{5}{3} + \frac{- 9 \cdot 3}{3}

$(\frac{2 y}{3}) + 2 y - \frac{5}{3} + \frac{- 9 \cdot 3}{3}$

Step 6

Combine the numerators over the common denominator.

(\frac{2 y}{3}) + 2 y + \frac{- 5 - 9 \cdot 3}{3}

$(\frac{2 y}{3}) + 2 y + \frac{- 5 - 9 \cdot 3}{3}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

- 9

$- 9$ by

3

$3$ .

(\frac{2 y}{3}) + 2 y + \frac{- 5 - 27}{3}

$(\frac{2 y}{3}) + 2 y + \frac{- 5 - 27}{3}$

Step 7.2

Subtract

27

$27$ from

- 5

$- 5$ .

(\frac{2 y}{3}) + 2 y + \frac{- 32}{3}

$(\frac{2 y}{3}) + 2 y + \frac{- 32}{3}$

(\frac{2 y}{3}) + 2 y + \frac{- 32}{3}

$(\frac{2 y}{3}) + 2 y + \frac{- 32}{3}$

Step 8

Move the negative in front of the fraction.

(\frac{2 y}{3}) + 2 y - \frac{32}{3}

$(\frac{2 y}{3}) + 2 y - \frac{32}{3}$

Step 9

To write

2 y

$2 y$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 y}{3} + 2 y \cdot \frac{3}{3} - \frac{32}{3}

$\frac{2 y}{3} + 2 y \cdot \frac{3}{3} - \frac{32}{3}$

Step 10

Combine

2 y

$2 y$ and

\frac{3}{3}

$\frac{3}{3}$ .

\frac{2 y}{3} + \frac{2 y \cdot 3}{3} - \frac{32}{3}

$\frac{2 y}{3} + \frac{2 y \cdot 3}{3} - \frac{32}{3}$

Step 11

Combine the numerators over the common denominator.

\frac{2 y + 2 y \cdot 3}{3} - \frac{32}{3}

$\frac{2 y + 2 y \cdot 3}{3} - \frac{32}{3}$

Step 12

Combine the numerators over the common denominator.

\frac{2 y + 2 y \cdot 3 - 32}{3}

$\frac{2 y + 2 y \cdot 3 - 32}{3}$

Step 13

Multiply

3

$3$ by

2

$2$ .

\frac{2 y + 6 y - 32}{3}

$\frac{2 y + 6 y - 32}{3}$

Step 14

Add

2 y

$2 y$ and

6 y

$6 y$ .

\frac{8 y - 32}{3}

$\frac{8 y - 32}{3}$

Step 15

Factor

8

$8$ out of

8 y - 32

$8 y - 32$ .

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Step 15.1

Factor

8

$8$ out of

8 y

$8 y$ .

\frac{8 (y) - 32}{3}

$\frac{8 (y) - 32}{3}$

Step 15.2

Factor

8

$8$ out of

- 32

$- 32$ .

\frac{8 y + 8 \cdot - 4}{3}

$\frac{8 y + 8 \cdot - 4}{3}$

Step 15.3

Factor

8

$8$ out of

8 y + 8 \cdot - 4

$8 y + 8 \cdot - 4$ .

\frac{8 (y - 4)}{3}

$\frac{8 (y - 4)}{3}$

\frac{8 (y - 4)}{3}

$\frac{8 (y - 4)}{3}$