Finite Math Examples

$7 \cdot (\frac{y \cdot 2 - 2 y \cdot 1 + y \cdot 0}{x^{2}}) - 2 \cdot \frac{y \cdot 2 - y \cdot 0}{2 x} - y \cdot 1 + x \cdot 1 y (0) = 5$ , $y (10) = 8$ , $x = 2$

Step 1

Replace all occurrences of $x$ with $2$ in each equation.

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Step 1.1

Replace all occurrences of $x$ in $\frac{7 \cdot 0}{x^{2}} + \frac{- 2 y \cdot 2}{2 x} - y + 0 = 5$ with $2$ .

$\frac{7 \cdot 0}{{(2)}^{2}} + \frac{- 2 y \cdot 2}{2 (2)} - y + 0 = 5$

$x = 2$

$y (10) = 8$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $\frac{7 \cdot 0}{{(2)}^{2}} + \frac{- 2 y \cdot 2}{2 (2)} - y + 0$ .

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Step 1.2.1.1

Simplify by adding terms.

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Step 1.2.1.1.1

Add $\frac{7 \cdot 0}{{(2)}^{2}} + \frac{- 2 y \cdot 2}{2 (2)} - y$ and $0$ .

$\frac{7 \cdot 0}{{(2)}^{2}} + \frac{- 2 y \cdot 2}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.1.2

Multiply $7$ by $0$ .

$\frac{0}{{(2)}^{2}} + \frac{- 2 y \cdot 2}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.1.3

Combine the opposite terms in $\frac{0}{{(2)}^{2}} + \frac{- 2 y \cdot 2}{2 (2)} - y$ .

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Step 1.2.1.1.3.1

Divide $0$ by ${(2)}^{2}$ .

$0 + \frac{- 2 y \cdot 2}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.1.3.2

Add $0$ and $\frac{- 2 y \cdot 2}{2 (2)}$ .

$\frac{- 2 y \cdot 2}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

$\frac{- 2 y \cdot 2}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

$\frac{- 2 y \cdot 2}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.2

Simplify each term.

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Step 1.2.1.2.1

Cancel the common factor of $- 2$ and $2$ .

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Step 1.2.1.2.1.1

Factor $2$ out of $- 2 y \cdot 2$ .

$\frac{2 (- y \cdot 2)}{2 (2)} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.2.1.2

Cancel the common factors.

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Step 1.2.1.2.1.2.1

Cancel the common factor.

$\frac{2 (- y \cdot 2)}{2 \cdot 2} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.2.1.2.2

Rewrite the expression.

$\frac{- y \cdot 2}{2} - y = 5$

$x = 2$

$y (10) = 8$

$\frac{- y \cdot 2}{2} - y = 5$

$x = 2$

$y (10) = 8$

$\frac{- y \cdot 2}{2} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.2.2

Cancel the common factor of $2$ .

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Step 1.2.1.2.2.1

Cancel the common factor.

$\frac{- y \cdot 2}{2} - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.2.2.2

Divide $- y$ by $1$ .

$- y - y = 5$

$x = 2$

$y (10) = 8$

$- y - y = 5$

$x = 2$

$y (10) = 8$

$- y - y = 5$

$x = 2$

$y (10) = 8$

Step 1.2.1.3

Subtract $y$ from $- y$ .

$- 2 y = 5$

$x = 2$

$y (10) = 8$

$- 2 y = 5$

$x = 2$

$y (10) = 8$

$- 2 y = 5$

$x = 2$

$y (10) = 8$

Step 1.3

Divide each term in $y (10) = 8$ by $10$ and simplify.

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Step 1.3.1

Divide each term in $y (10) = 8$ by $10$ .

$\frac{y \cdot 10}{10} = \frac{8}{10}$

$- 2 y = 5$

$x = 2$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $10$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{y \cdot 10}{10} = \frac{8}{10}$

$- 2 y = 5$

$x = 2$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{10}$

$- 2 y = 5$

$x = 2$

$y = \frac{8}{10}$

$- 2 y = 5$

$x = 2$

$y = \frac{8}{10}$

$- 2 y = 5$

$x = 2$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Cancel the common factor of $8$ and $10$ .

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Step 1.3.3.1.1

Factor $2$ out of $8$ .

$y = \frac{2 (4)}{10}$

$- 2 y = 5$

$x = 2$

Step 1.3.3.1.2

Cancel the common factors.

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Step 1.3.3.1.2.1

Factor $2$ out of $10$ .

$y = \frac{2 \cdot 4}{2 \cdot 5}$

$- 2 y = 5$

$x = 2$

Step 1.3.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 4}{2 \cdot 5}$

$- 2 y = 5$

$x = 2$

Step 1.3.3.1.2.3

Rewrite the expression.

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

$- 2 y = 5$

$x = 2$

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

$- 2 y = 5$

$x = 2$

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

$- 2 y = 5$

$x = 2$

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

$- 2 y = 5$

$x = 2$

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

$- 2 y = 5$

$x = 2$

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

$- 2 y = 5$

$x = 2$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $- 2 y = 5$ with $\frac{4}{5}$ .

$- 2 (\frac{4}{5}) = 5$

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

$x = 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 2 (\frac{4}{5})$ .

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Step 2.2.1.1

Multiply $- 2 (\frac{4}{5})$ .

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Step 2.2.1.1.1

Combine $- 2$ and $\frac{4}{5}$ .

$\frac{- 2 \cdot 4}{5} = 5$

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

$x = 2$

Step 2.2.1.1.2

Multiply $- 2$ by $4$ .

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

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

$x = 2$

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

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

$x = 2$

Step 2.2.1.2

Move the negative in front of the fraction.

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

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

$x = 2$

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

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

$x = 2$

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

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

$x = 2$

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

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

$x = 2$

Step 3

Since $- \frac{8}{5} = 5$ is not true, there is no solution.

No solution

Step 4