Finite Math Examples

$25 x - 30 y + 100 = 0$ , $50 x + 40 y - 200 = 0$

Step 1

Solve for $x$ in $25 x - 30 y + 100 = 0$ .

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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

Add $30 y$ to both sides of the equation.

$25 x + 100 = 30 y$

$50 x + 40 y - 200 = 0$

Step 1.1.2

Subtract $100$ from both sides of the equation.

$25 x = 30 y - 100$

$50 x + 40 y - 200 = 0$

$25 x = 30 y - 100$

$50 x + 40 y - 200 = 0$

Step 1.2

Divide each term in $25 x = 30 y - 100$ by $25$ and simplify.

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Step 1.2.1

Divide each term in $25 x = 30 y - 100$ by $25$ .

$\frac{25 x}{25} = \frac{30 y}{25} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $25$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{25 x}{25} = \frac{30 y}{25} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{30 y}{25} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

$x = \frac{30 y}{25} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

$x = \frac{30 y}{25} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

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

Cancel the common factor of $30$ and $25$ .

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Step 1.2.3.1.1.1

Factor $5$ out of $30 y$ .

$x = \frac{5 (6 y)}{25} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $5$ out of $25$ .

$x = \frac{5 (6 y)}{5 (5)} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{5 (6 y)}{5 \cdot 5} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{6 y}{5} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

$x = \frac{6 y}{5} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

$x = \frac{6 y}{5} + \frac{- 100}{25}$

$50 x + 40 y - 200 = 0$

Step 1.2.3.1.2

Divide $- 100$ by $25$ .

$x = \frac{6 y}{5} - 4$

$50 x + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

$50 x + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

$50 x + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

$50 x + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

$50 x + 40 y - 200 = 0$

Step 2

Replace all occurrences of $x$ with $\frac{6 y}{5} - 4$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $50 x + 40 y - 200 = 0$ with $\frac{6 y}{5} - 4$ .

$50 (\frac{6 y}{5} - 4) + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $50 (\frac{6 y}{5} - 4) + 40 y - 200$ .

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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.

$50 (\frac{6 y}{5}) + 50 \cdot - 4 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.1.2.1

Factor $5$ out of $50$ .

$5 (10) (\frac{6 y}{5}) + 50 \cdot - 4 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.1.2.2

Cancel the common factor.

$5 \cdot (10 (\frac{6 y}{5})) + 50 \cdot - 4 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.1.2.3

Rewrite the expression.

$10 (6 y) + 50 \cdot - 4 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

$10 (6 y) + 50 \cdot - 4 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.1.3

Multiply $6$ by $10$ .

$60 y + 50 \cdot - 4 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.1.4

Multiply $50$ by $- 4$ .

$60 y - 200 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

$60 y - 200 + 40 y - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $60 y$ and $40 y$ .

$100 y - 200 - 200 = 0$

$x = \frac{6 y}{5} - 4$

Step 2.2.1.2.2

Subtract $200$ from $- 200$ .

$100 y - 400 = 0$

$x = \frac{6 y}{5} - 4$

$100 y - 400 = 0$

$x = \frac{6 y}{5} - 4$

$100 y - 400 = 0$

$x = \frac{6 y}{5} - 4$

$100 y - 400 = 0$

$x = \frac{6 y}{5} - 4$

$100 y - 400 = 0$

$x = \frac{6 y}{5} - 4$

Step 3

Solve for $y$ in $100 y - 400 = 0$ .

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Step 3.1

Add $400$ to both sides of the equation.

$100 y = 400$

$x = \frac{6 y}{5} - 4$

Step 3.2

Divide each term in $100 y = 400$ by $100$ and simplify.

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Step 3.2.1

Divide each term in $100 y = 400$ by $100$ .

$\frac{100 y}{100} = \frac{400}{100}$

$x = \frac{6 y}{5} - 4$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $100$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{100 y}{100} = \frac{400}{100}$

$x = \frac{6 y}{5} - 4$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{400}{100}$

$x = \frac{6 y}{5} - 4$

$y = \frac{400}{100}$

$x = \frac{6 y}{5} - 4$

$y = \frac{400}{100}$

$x = \frac{6 y}{5} - 4$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $400$ by $100$ .

$y = 4$

$x = \frac{6 y}{5} - 4$

$y = 4$

$x = \frac{6 y}{5} - 4$

$y = 4$

$x = \frac{6 y}{5} - 4$

$y = 4$

$x = \frac{6 y}{5} - 4$

Step 4

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

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Step 4.1

Replace all occurrences of $y$ in $x = \frac{6 y}{5} - 4$ with $4$ .

$x = \frac{6 (4)}{5} - 4$

$y = 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{6 (4)}{5} - 4$ .

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Step 4.2.1.1

Multiply $6$ by $4$ .

$x = \frac{24}{5} - 4$

$y = 4$

Step 4.2.1.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = \frac{24}{5} - 4 \cdot \frac{5}{5}$

$y = 4$

Step 4.2.1.3

Combine $- 4$ and $\frac{5}{5}$ .

$x = \frac{24}{5} + \frac{- 4 \cdot 5}{5}$

$y = 4$

Step 4.2.1.4

Combine the numerators over the common denominator.

$x = \frac{24 - 4 \cdot 5}{5}$

$y = 4$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $- 4$ by $5$ .

$x = \frac{24 - 20}{5}$

$y = 4$

Step 4.2.1.5.2

Subtract $20$ from $24$ .

$x = \frac{4}{5}$

$y = 4$

$x = \frac{4}{5}$

$y = 4$

$x = \frac{4}{5}$

$y = 4$

$x = \frac{4}{5}$

$y = 4$

$x = \frac{4}{5}$

$y = 4$

Step 5

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

$(\frac{4}{5}, 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(\frac{4}{5}, 4)$

Equation Form:

$x = \frac{4}{5}, y = 4$

Step 7