Finite Math Examples

$2 y = x + 8$ , $x - 2 y = - 8$

Step 1

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

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Step 1.1

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

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

$x - 2 y = - 8$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

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

$x - 2 y = - 8$

Step 1.2.1.2

Divide $y$ by $1$ .

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

$x - 2 y = - 8$

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

$x - 2 y = - 8$

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

$x - 2 y = - 8$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $8$ by $2$ .

$y = \frac{x}{2} + 4$

$x - 2 y = - 8$

$y = \frac{x}{2} + 4$

$x - 2 y = - 8$

$y = \frac{x}{2} + 4$

$x - 2 y = - 8$

Step 2

Replace all occurrences of $y$ with $\frac{x}{2} + 4$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $x - 2 y = - 8$ with $\frac{x}{2} + 4$ .

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

$y = \frac{x}{2} + 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$x - 2 \frac{x}{2} - 2 \cdot 4 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Factor $2$ out of $- 2$ .

$x + 2 (- 1) (\frac{x}{2}) - 2 \cdot 4 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.1.2.2

Cancel the common factor.

$x + 2 \cdot (- 1 \frac{x}{2}) - 2 \cdot 4 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.1.2.3

Rewrite the expression.

$x - 1 x - 2 \cdot 4 = - 8$

$y = \frac{x}{2} + 4$

$x - 1 x - 2 \cdot 4 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.1.3

Multiply $- 2$ by $4$ .

$x - 1 x - 8 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.1.4

Rewrite $- 1 x$ as $- x$ .

$x - x - 8 = - 8$

$y = \frac{x}{2} + 4$

$x - x - 8 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $x$ from $x$ .

$0 - 8 = - 8$

$y = \frac{x}{2} + 4$

Step 2.2.1.2.2

Subtract $8$ from $0$ .

$- 8 = - 8$

$y = \frac{x}{2} + 4$

$- 8 = - 8$

$y = \frac{x}{2} + 4$

$- 8 = - 8$

$y = \frac{x}{2} + 4$

$- 8 = - 8$

$y = \frac{x}{2} + 4$

$- 8 = - 8$

$y = \frac{x}{2} + 4$

Step 3

Remove any equations from the system that are always true.

$y = \frac{x}{2} + 4$

Step 4