Finite Math Examples

$9 x - 6 y = - 24$ , $9 x = 6 y - 24$

Step 1

Divide each term in $9 x = 6 y - 24$ by $9$ and simplify.

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Step 1.1

Divide each term in $9 x = 6 y - 24$ by $9$ .

$\frac{9 x}{9} = \frac{6 y}{9} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $9$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{6 y}{9} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{6 y}{9} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

$x = \frac{6 y}{9} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

$x = \frac{6 y}{9} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $6$ and $9$ .

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Step 1.3.1.1.1

Factor $3$ out of $6 y$ .

$x = \frac{3 (2 y)}{9} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $3$ out of $9$ .

$x = \frac{3 (2 y)}{3 (3)} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.3.1.1.2.2

Cancel the common factor.

$x = \frac{3 (2 y)}{3 \cdot 3} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.3.1.1.2.3

Rewrite the expression.

$x = \frac{2 y}{3} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} + \frac{- 24}{9}$

$9 x - 6 y = - 24$

Step 1.3.1.2

Cancel the common factor of $- 24$ and $9$ .

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Step 1.3.1.2.1

Factor $3$ out of $- 24$ .

$x = \frac{2 y}{3} + \frac{3 (- 8)}{9}$

$9 x - 6 y = - 24$

Step 1.3.1.2.2

Cancel the common factors.

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Step 1.3.1.2.2.1

Factor $3$ out of $9$ .

$x = \frac{2 y}{3} + \frac{3 \cdot - 8}{3 \cdot 3}$

$9 x - 6 y = - 24$

Step 1.3.1.2.2.2

Cancel the common factor.

$x = \frac{2 y}{3} + \frac{3 \cdot - 8}{3 \cdot 3}$

$9 x - 6 y = - 24$

Step 1.3.1.2.2.3

Rewrite the expression.

$x = \frac{2 y}{3} + \frac{- 8}{3}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} + \frac{- 8}{3}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} + \frac{- 8}{3}$

$9 x - 6 y = - 24$

Step 1.3.1.3

Move the negative in front of the fraction.

$x = \frac{2 y}{3} - \frac{8}{3}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$9 x - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$9 x - 6 y = - 24$

Step 2

Replace all occurrences of $x$ with $\frac{2 y}{3} - \frac{8}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $9 x - 6 y = - 24$ with $\frac{2 y}{3} - \frac{8}{3}$ .

$9 (\frac{2 y}{3} - \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $9 (\frac{2 y}{3} - \frac{8}{3}) - 6 y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$9 (\frac{2 y}{3}) + 9 (- \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Factor $3$ out of $9$ .

$3 (3) (\frac{2 y}{3}) + 9 (- \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.2.2

Cancel the common factor.

$3 \cdot (3 (\frac{2 y}{3})) + 9 (- \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.2.3

Rewrite the expression.

$3 (2 y) + 9 (- \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$3 (2 y) + 9 (- \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.3

Multiply $2$ by $3$ .

$6 y + 9 (- \frac{8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.4

Cancel the common factor of $3$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$6 y + 9 (\frac{- 8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.4.2

Factor $3$ out of $9$ .

$6 y + 3 (3) (\frac{- 8}{3}) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.4.3

Cancel the common factor.

$6 y + 3 \cdot (3 (\frac{- 8}{3})) - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.4.4

Rewrite the expression.

$6 y + 3 \cdot - 8 - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$6 y + 3 \cdot - 8 - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.1.5

Multiply $3$ by $- 8$ .

$6 y - 24 - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$6 y - 24 - 6 y = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.2

Combine the opposite terms in $6 y - 24 - 6 y$ .

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Step 2.2.1.2.1

Subtract $6 y$ from $6 y$ .

$0 - 24 = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 2.2.1.2.2

Subtract $24$ from $0$ .

$- 24 = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$- 24 = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$- 24 = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$- 24 = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

$- 24 = - 24$

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{2 y}{3} - \frac{8}{3}$

Step 4