Finite Math Examples

$4 x + 0 y = 3$ , $0 x + 7 y = - 5$

Step 1

Divide each term in $4 x = 3$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 x = 3$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4}$

$7 y = - 5$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4}$

$7 y = - 5$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{4}$

$7 y = - 5$

$x = \frac{3}{4}$

$7 y = - 5$

$x = \frac{3}{4}$

$7 y = - 5$

$x = \frac{3}{4}$

$7 y = - 5$

Step 2

Divide each term in $7 y = - 5$ by $7$ and simplify.

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Step 2.1

Divide each term in $7 y = - 5$ by $7$ .

$\frac{7 y}{7} = \frac{- 5}{7}$

$x = \frac{3}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 5}{7}$

$x = \frac{3}{4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{7}$

$x = \frac{3}{4}$

$y = \frac{- 5}{7}$

$x = \frac{3}{4}$

$y = \frac{- 5}{7}$

$x = \frac{3}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$y = - \frac{5}{7}$

$x = \frac{3}{4}$

$y = - \frac{5}{7}$

$x = \frac{3}{4}$

$y = - \frac{5}{7}$

$x = \frac{3}{4}$

Step 3

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

$(\frac{3}{4}, - \frac{5}{7})$

Step 4

The result can be shown in multiple forms.

Point Form:

$(\frac{3}{4}, - \frac{5}{7})$

Equation Form:

$x = \frac{3}{4}, y = - \frac{5}{7}$

Step 5