Finite Math Examples

$2 x + 5 y = 400$ , $100 x + 80 = 13200$

Step 1

Solve for $x$ in $100 x + 80 = 13200$ .

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Step 1.1

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

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Step 1.1.1

Subtract $80$ from both sides of the equation.

$100 x = 13200 - 80$

$2 x + 5 y = 400$

Step 1.1.2

Subtract $80$ from $13200$ .

$100 x = 13120$

$2 x + 5 y = 400$

$100 x = 13120$

$2 x + 5 y = 400$

Step 1.2

Divide each term in $100 x = 13120$ by $100$ and simplify.

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Step 1.2.1

Divide each term in $100 x = 13120$ by $100$ .

$\frac{100 x}{100} = \frac{13120}{100}$

$2 x + 5 y = 400$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $100$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{100 x}{100} = \frac{13120}{100}$

$2 x + 5 y = 400$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{13120}{100}$

$2 x + 5 y = 400$

$x = \frac{13120}{100}$

$2 x + 5 y = 400$

$x = \frac{13120}{100}$

$2 x + 5 y = 400$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $13120$ and $100$ .

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Step 1.2.3.1.1

Factor $20$ out of $13120$ .

$x = \frac{20 (656)}{100}$

$2 x + 5 y = 400$

Step 1.2.3.1.2

Cancel the common factors.

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Step 1.2.3.1.2.1

Factor $20$ out of $100$ .

$x = \frac{20 \cdot 656}{20 \cdot 5}$

$2 x + 5 y = 400$

Step 1.2.3.1.2.2

Cancel the common factor.

$x = \frac{20 \cdot 656}{20 \cdot 5}$

$2 x + 5 y = 400$

Step 1.2.3.1.2.3

Rewrite the expression.

$x = \frac{656}{5}$

$2 x + 5 y = 400$

$x = \frac{656}{5}$

$2 x + 5 y = 400$

$x = \frac{656}{5}$

$2 x + 5 y = 400$

$x = \frac{656}{5}$

$2 x + 5 y = 400$

$x = \frac{656}{5}$

$2 x + 5 y = 400$

$x = \frac{656}{5}$

$2 x + 5 y = 400$

Step 2

Replace all occurrences of $x$ with $\frac{656}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2 x + 5 y = 400$ with $\frac{656}{5}$ .

$2 (\frac{656}{5}) + 5 y = 400$

$x = \frac{656}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $2 (\frac{656}{5})$ .

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Step 2.2.1.1

Combine $2$ and $\frac{656}{5}$ .

$\frac{2 \cdot 656}{5} + 5 y = 400$

$x = \frac{656}{5}$

Step 2.2.1.2

Multiply $2$ by $656$ .

$\frac{1312}{5} + 5 y = 400$

$x = \frac{656}{5}$

$\frac{1312}{5} + 5 y = 400$

$x = \frac{656}{5}$

$\frac{1312}{5} + 5 y = 400$

$x = \frac{656}{5}$

$\frac{1312}{5} + 5 y = 400$

$x = \frac{656}{5}$

Step 3

Solve for $y$ in $\frac{1312}{5} + 5 y = 400$ .

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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 $\frac{1312}{5}$ from both sides of the equation.

$5 y = 400 - \frac{1312}{5}$

$x = \frac{656}{5}$

Step 3.1.2

To write $400$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$5 y = 400 \cdot \frac{5}{5} - \frac{1312}{5}$

$x = \frac{656}{5}$

Step 3.1.3

Combine $400$ and $\frac{5}{5}$ .

$5 y = \frac{400 \cdot 5}{5} - \frac{1312}{5}$

$x = \frac{656}{5}$

Step 3.1.4

Combine the numerators over the common denominator.

$5 y = \frac{400 \cdot 5 - 1312}{5}$

$x = \frac{656}{5}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $400$ by $5$ .

$5 y = \frac{2000 - 1312}{5}$

$x = \frac{656}{5}$

Step 3.1.5.2

Subtract $1312$ from $2000$ .

$5 y = \frac{688}{5}$

$x = \frac{656}{5}$

$5 y = \frac{688}{5}$

$x = \frac{656}{5}$

$5 y = \frac{688}{5}$

$x = \frac{656}{5}$

Step 3.2

Divide each term in $5 y = \frac{688}{5}$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 y = \frac{688}{5}$ by $5$ .

$\frac{5 y}{5} = \frac{\frac{688}{5}}{5}$

$x = \frac{656}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{\frac{688}{5}}{5}$

$x = \frac{656}{5}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{688}{5}}{5}$

$x = \frac{656}{5}$

$y = \frac{\frac{688}{5}}{5}$

$x = \frac{656}{5}$

$y = \frac{\frac{688}{5}}{5}$

$x = \frac{656}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{688}{5} \cdot \frac{1}{5}$

$x = \frac{656}{5}$

Step 3.2.3.2

Multiply $\frac{688}{5} \cdot \frac{1}{5}$ .

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Step 3.2.3.2.1

Multiply $\frac{688}{5}$ by $\frac{1}{5}$ .

$y = \frac{688}{5 \cdot 5}$

$x = \frac{656}{5}$

Step 3.2.3.2.2

Multiply $5$ by $5$ .

$y = \frac{688}{25}$

$x = \frac{656}{5}$

$y = \frac{688}{25}$

$x = \frac{656}{5}$

$y = \frac{688}{25}$

$x = \frac{656}{5}$

$y = \frac{688}{25}$

$x = \frac{656}{5}$

$y = \frac{688}{25}$

$x = \frac{656}{5}$

Step 4

Solve the system of equations.

$y = \frac{688}{25} x = \frac{656}{5}$

Step 5

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

$(\frac{656}{5}, \frac{688}{25})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{656}{5}, \frac{688}{25})$

Equation Form:

$x = \frac{656}{5}, y = \frac{688}{25}$

Step 7