Finite Math Examples

$4 x + 4 y = 16$ , $5 x - 3 y = 15$

Step 1

Solve for $x$ in $4 x + 4 y = 16$ .

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Step 1.1

Subtract $4 y$ from both sides of the equation.

$4 x = 16 - 4 y$

$5 x - 3 y = 15$

Step 1.2

Divide each term in $4 x = 16 - 4 y$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x = 16 - 4 y$ by $4$ .

$\frac{4 x}{4} = \frac{16}{4} + \frac{- 4 y}{4}$

$5 x - 3 y = 15$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{16}{4} + \frac{- 4 y}{4}$

$5 x - 3 y = 15$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{16}{4} + \frac{- 4 y}{4}$

$5 x - 3 y = 15$

$x = \frac{16}{4} + \frac{- 4 y}{4}$

$5 x - 3 y = 15$

$x = \frac{16}{4} + \frac{- 4 y}{4}$

$5 x - 3 y = 15$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $16$ by $4$ .

$x = 4 + \frac{- 4 y}{4}$

$5 x - 3 y = 15$

Step 1.2.3.1.2

Cancel the common factor of $- 4$ and $4$ .

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Step 1.2.3.1.2.1

Factor $4$ out of $- 4 y$ .

$x = 4 + \frac{4 (- y)}{4}$

$5 x - 3 y = 15$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $4$ out of $4$ .

$x = 4 + \frac{4 (- y)}{4 (1)}$

$5 x - 3 y = 15$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = 4 + \frac{4 (- y)}{4 \cdot 1}$

$5 x - 3 y = 15$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = 4 + \frac{- y}{1}$

$5 x - 3 y = 15$

Step 1.2.3.1.2.2.4

Divide $- y$ by $1$ .

$x = 4 - y$

$5 x - 3 y = 15$

$x = 4 - y$

$5 x - 3 y = 15$

$x = 4 - y$

$5 x - 3 y = 15$

$x = 4 - y$

$5 x - 3 y = 15$

$x = 4 - y$

$5 x - 3 y = 15$

$x = 4 - y$

$5 x - 3 y = 15$

$x = 4 - y$

$5 x - 3 y = 15$

Step 2

Replace all occurrences of $x$ with $4 - y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $5 x - 3 y = 15$ with $4 - y$ .

$5 (4 - y) - 3 y = 15$

$x = 4 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (4 - y) - 3 y$ .

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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.

$5 \cdot 4 + 5 (- y) - 3 y = 15$

$x = 4 - y$

Step 2.2.1.1.2

Multiply $5$ by $4$ .

$20 + 5 (- y) - 3 y = 15$

$x = 4 - y$

Step 2.2.1.1.3

Multiply $- 1$ by $5$ .

$20 - 5 y - 3 y = 15$

$x = 4 - y$

$20 - 5 y - 3 y = 15$

$x = 4 - y$

Step 2.2.1.2

Subtract $3 y$ from $- 5 y$ .

$20 - 8 y = 15$

$x = 4 - y$

$20 - 8 y = 15$

$x = 4 - y$

$20 - 8 y = 15$

$x = 4 - y$

$20 - 8 y = 15$

$x = 4 - y$

Step 3

Solve for $y$ in $20 - 8 y = 15$ .

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Step 3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1.1

Subtract $20$ from both sides of the equation.

$- 8 y = 15 - 20$

$x = 4 - y$

Step 3.1.2

Subtract $20$ from $15$ .

$- 8 y = - 5$

$x = 4 - y$

$- 8 y = - 5$

$x = 4 - y$

Step 3.2

Divide each term in $- 8 y = - 5$ by $- 8$ and simplify.

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Step 3.2.1

Divide each term in $- 8 y = - 5$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 5}{- 8}$

$x = 4 - y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 5}{- 8}$

$x = 4 - y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5}{- 8}$

$x = 4 - y$

$y = \frac{- 5}{- 8}$

$x = 4 - y$

$y = \frac{- 5}{- 8}$

$x = 4 - y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Dividing two negative values results in a positive value.

$y = \frac{5}{8}$

$x = 4 - y$

$y = \frac{5}{8}$

$x = 4 - y$

$y = \frac{5}{8}$

$x = 4 - y$

$y = \frac{5}{8}$

$x = 4 - y$

Step 4

Replace all occurrences of $y$ with $\frac{5}{8}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 4 - y$ with $\frac{5}{8}$ .

$x = 4 - (\frac{5}{8})$

$y = \frac{5}{8}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $4 - (\frac{5}{8})$ .

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Step 4.2.1.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$x = 4 \cdot \frac{8}{8} - \frac{5}{8}$

$y = \frac{5}{8}$

Step 4.2.1.2

Combine $4$ and $\frac{8}{8}$ .

$x = \frac{4 \cdot 8}{8} - \frac{5}{8}$

$y = \frac{5}{8}$

Step 4.2.1.3

Combine the numerators over the common denominator.

$x = \frac{4 \cdot 8 - 5}{8}$

$y = \frac{5}{8}$

Step 4.2.1.4

Simplify the numerator.

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Step 4.2.1.4.1

Multiply $4$ by $8$ .

$x = \frac{32 - 5}{8}$

$y = \frac{5}{8}$

Step 4.2.1.4.2

Subtract $5$ from $32$ .

$x = \frac{27}{8}$

$y = \frac{5}{8}$

$x = \frac{27}{8}$

$y = \frac{5}{8}$

$x = \frac{27}{8}$

$y = \frac{5}{8}$

$x = \frac{27}{8}$

$y = \frac{5}{8}$

$x = \frac{27}{8}$

$y = \frac{5}{8}$

Step 5

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

$(\frac{27}{8}, \frac{5}{8})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{27}{8}, \frac{5}{8})$

Equation Form:

$x = \frac{27}{8}, y = \frac{5}{8}$

Step 7