Finite Math Examples

$- 3 x - 2 y = 0$ , $3 x - y = 8$

Step 1

Solve for $x$ in $- 3 x - 2 y = 0$ .

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Step 1.1

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

$- 3 x = 2 y$

$3 x - y = 8$

Step 1.2

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

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Step 1.2.1

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

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

$3 x - y = 8$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

$3 x - y = 8$

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

$3 x - y = 8$

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

$3 x - y = 8$

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

$3 x - y = 8$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

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

$3 x - y = 8$

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

$3 x - y = 8$

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

$3 x - y = 8$

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

$3 x - y = 8$

Step 2

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

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Step 2.1

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

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

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

Step 2.2.1.1.2

Cancel the common factor.

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

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

Step 2.2.1.1.3

Rewrite the expression.

$- 2 y - y = 8$

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

$- 2 y - y = 8$

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

Step 2.2.1.2

Subtract $y$ from $- 2 y$ .

$- 3 y = 8$

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

$- 3 y = 8$

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

$- 3 y = 8$

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

$- 3 y = 8$

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

Step 3

Divide each term in $- 3 y = 8$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y = 8$ by $- 3$ .

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

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

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

Step 3.2.1.2

Divide $y$ by $1$ .

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

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

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

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

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

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

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

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

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

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

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

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

Step 4

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

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Step 4.1

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

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

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

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Simplify the numerator.

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Step 4.2.1.1.1

Multiply $- 1$ by $2$ .

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

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

Step 4.2.1.1.2

Combine $- 2$ and $\frac{8}{3}$ .

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

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

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

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

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $- 2$ by $8$ .

$x = - \frac{\frac{- 16}{3}}{3}$

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

Step 4.2.1.2.2

Move the negative in front of the fraction.

$x = - \frac{- \frac{16}{3}}{3}$

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

$x = - \frac{- \frac{16}{3}}{3}$

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

Step 4.2.1.3

Multiply the numerator by the reciprocal of the denominator.

$x = - (- \frac{16}{3} \cdot \frac{1}{3})$

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

Step 4.2.1.4

Multiply $- \frac{16}{3} \cdot \frac{1}{3}$ .

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Step 4.2.1.4.1

Multiply $\frac{1}{3}$ by $\frac{16}{3}$ .

$x = \frac{16}{3 \cdot 3}$

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

Step 4.2.1.4.2

Multiply $3$ by $3$ .

$x = \frac{16}{9}$

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

$x = \frac{16}{9}$

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

Step 4.2.1.5

Multiply $- - \frac{16}{9}$ .

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Step 4.2.1.5.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{16}{9})$

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

Step 4.2.1.5.2

Multiply $\frac{16}{9}$ by $1$ .

$x = \frac{16}{9}$

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

$x = \frac{16}{9}$

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

$x = \frac{16}{9}$

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

$x = \frac{16}{9}$

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

$x = \frac{16}{9}$

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

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(\frac{16}{9}, - \frac{8}{3})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{16}{9}, - \frac{8}{3})$

Equation Form:

$x = \frac{16}{9}, y = - \frac{8}{3}$

Step 7