Finite Math Examples

$3 x - 2 y = - 5$ , $x + 2 y - 9$

Step 1

Add $2 y$ to both sides of the equation.

$3 x = - 5 + 2 y$

Step 2

Divide each term in $3 x = - 5 + 2 y$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x = - 5 + 2 y$ by $3$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

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

Step 3

Replace the variable $x$ with $- \frac{5}{3} + \frac{2 y}{3}$ in the expression.

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

Step 4

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 5

Combine $- 9$ and $\frac{3}{3}$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 9$ by $3$ .

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

Step 7.2

Subtract $27$ from $- 5$ .

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

Step 8

Move the negative in front of the fraction.

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

Step 9

To write $2 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 10

Combine $2 y$ and $\frac{3}{3}$ .

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

Step 11

Combine the numerators over the common denominator.

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

Step 12

Combine the numerators over the common denominator.

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

Step 13

Multiply $3$ by $2$ .

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

Step 14

Add $2 y$ and $6 y$ .

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

Step 15

Factor $8$ out of $8 y - 32$ .

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Step 15.1

Factor $8$ out of $8 y$ .

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

Step 15.2

Factor $8$ out of $- 32$ .

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

Step 15.3

Factor $8$ out of $8 y + 8 \cdot - 4$ .

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