Finite Math Examples

$8 x + 2 y = 17$ , $- 4 x - y = 9$

Step 1

Solve for $x$ in $8 x + 2 y = 17$ .

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Step 1.1

Subtract $2 y$ from both sides of the equation.

$8 x = 17 - 2 y$

$- 4 x - y = 9$

Step 1.2

Divide each term in $8 x = 17 - 2 y$ by $8$ and simplify.

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Step 1.2.1

Divide each term in $8 x = 17 - 2 y$ by $8$ .

$\frac{8 x}{8} = \frac{17}{8} + \frac{- 2 y}{8}$

$- 4 x - y = 9$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{17}{8} + \frac{- 2 y}{8}$

$- 4 x - y = 9$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{17}{8} + \frac{- 2 y}{8}$

$- 4 x - y = 9$

$x = \frac{17}{8} + \frac{- 2 y}{8}$

$- 4 x - y = 9$

$x = \frac{17}{8} + \frac{- 2 y}{8}$

$- 4 x - y = 9$

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 $- 2$ and $8$ .

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Step 1.2.3.1.1.1

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

$x = \frac{17}{8} + \frac{2 (- y)}{8}$

$- 4 x - y = 9$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $8$ .

$x = \frac{17}{8} + \frac{2 (- y)}{2 (4)}$

$- 4 x - y = 9$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$x = \frac{17}{8} + \frac{2 (- y)}{2 \cdot 4}$

$- 4 x - y = 9$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$x = \frac{17}{8} + \frac{- y}{4}$

$- 4 x - y = 9$

$x = \frac{17}{8} + \frac{- y}{4}$

$- 4 x - y = 9$

$x = \frac{17}{8} + \frac{- y}{4}$

$- 4 x - y = 9$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x = \frac{17}{8} - \frac{y}{4}$

$- 4 x - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- 4 x - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- 4 x - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- 4 x - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- 4 x - y = 9$

Step 2

Replace all occurrences of $x$ with $\frac{17}{8} - \frac{y}{4}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 4 x - y = 9$ with $\frac{17}{8} - \frac{y}{4}$ .

$- 4 (\frac{17}{8} - \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 4 (\frac{17}{8} - \frac{y}{4}) - y$ .

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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.

$- 4 (\frac{17}{8}) - 4 (- \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Factor $4$ out of $- 4$ .

$4 (- 1) (\frac{17}{8}) - 4 (- \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.2.2

Factor $4$ out of $8$ .

$4 \cdot (- 1 \frac{17}{4 \cdot 2}) - 4 (- \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.2.3

Cancel the common factor.

$4 \cdot (- 1 \frac{17}{4 \cdot 2}) - 4 (- \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.2.4

Rewrite the expression.

$- 1 (\frac{17}{2}) - 4 (- \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- 1 (\frac{17}{2}) - 4 (- \frac{y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.3

Cancel the common factor of $4$ .

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Step 2.2.1.1.3.1

Move the leading negative in $- \frac{y}{4}$ into the numerator.

$- 1 (\frac{17}{2}) - 4 \frac{- y}{4} - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.3.2

Factor $4$ out of $- 4$ .

$- 1 (\frac{17}{2}) + 4 (- 1) (\frac{- y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.3.3

Cancel the common factor.

$- 1 (\frac{17}{2}) + 4 \cdot (- 1 \frac{- y}{4}) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.3.4

Rewrite the expression.

$- 1 (\frac{17}{2}) - 1 (- y) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- 1 (\frac{17}{2}) - 1 (- y) - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.4

Multiply $- 1$ by $- 1$ .

$- 1 (\frac{17}{2}) + 1 y - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.5

Multiply $y$ by $1$ .

$- 1 (\frac{17}{2}) + y - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.1.6

Rewrite $- 1 (\frac{17}{2})$ as $- (\frac{17}{2})$ .

$- \frac{17}{2} + y - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- \frac{17}{2} + y - y = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.2

Combine the opposite terms in $- \frac{17}{2} + y - y$ .

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Step 2.2.1.2.1

Subtract $y$ from $y$ .

$- \frac{17}{2} + 0 = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 2.2.1.2.2

Add $- \frac{17}{2}$ and $0$ .

$- \frac{17}{2} = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- \frac{17}{2} = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- \frac{17}{2} = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- \frac{17}{2} = 9$

$x = \frac{17}{8} - \frac{y}{4}$

$- \frac{17}{2} = 9$

$x = \frac{17}{8} - \frac{y}{4}$

Step 3

Since $- \frac{17}{2} = 9$ is not true, there is no solution.

No solution

Step 4