Finite Math Examples

$5 x + 0 y = 2$ , $0 x + 9 y = - 5$

Step 1

Divide each term in $5 x = 2$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 x = 2$ by $5$ .

$\frac{5 x}{5} = \frac{2}{5}$

$9 y = - 5$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{2}{5}$

$9 y = - 5$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{5}$

$9 y = - 5$

$x = \frac{2}{5}$

$9 y = - 5$

$x = \frac{2}{5}$

$9 y = - 5$

$x = \frac{2}{5}$

$9 y = - 5$

Step 2

Divide each term in $9 y = - 5$ by $9$ and simplify.

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Step 2.1

Divide each term in $9 y = - 5$ by $9$ .

$\frac{9 y}{9} = \frac{- 5}{9}$

$x = \frac{2}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 5}{9}$

$x = \frac{2}{5}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{9}$

$x = \frac{2}{5}$

$y = \frac{- 5}{9}$

$x = \frac{2}{5}$

$y = \frac{- 5}{9}$

$x = \frac{2}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$y = - \frac{5}{9}$

$x = \frac{2}{5}$

$y = - \frac{5}{9}$

$x = \frac{2}{5}$

$y = - \frac{5}{9}$

$x = \frac{2}{5}$

Step 3

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

$(\frac{2}{5}, - \frac{5}{9})$

Step 4

The result can be shown in multiple forms.

Point Form:

$(\frac{2}{5}, - \frac{5}{9})$

Equation Form:

$x = \frac{2}{5}, y = - \frac{5}{9}$

Step 5