Finite Math Examples

$y = - \frac{1}{4} x + 1$ , $- x - 4 y = - 4$

Step 1

Combine $x$ and $\frac{1}{4}$ .

$y = - \frac{x}{4} + 1$

$- x - 4 y = - 4$

Step 2

Replace all occurrences of $y$ with $- \frac{x}{4} + 1$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- x - 4 y = - 4$ with $- \frac{x}{4} + 1$ .

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

$y = - \frac{x}{4} + 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- x - 4 (- \frac{x}{4} + 1)$ .

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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.

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

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

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

$- x - 4 \frac{- x}{4} - 4 \cdot 1 = - 4$

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.2.2

Factor $4$ out of $- 4$ .

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

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.2.3

Cancel the common factor.

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

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.2.4

Rewrite the expression.

$- x - 1 (- x) - 4 \cdot 1 = - 4$

$y = - \frac{x}{4} + 1$

$- x - 1 (- x) - 4 \cdot 1 = - 4$

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.3

Multiply $- 1$ by $- 1$ .

$- x + 1 x - 4 \cdot 1 = - 4$

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.4

Multiply $x$ by $1$ .

$- x + x - 4 \cdot 1 = - 4$

$y = - \frac{x}{4} + 1$

Step 2.2.1.1.5

Multiply $- 4$ by $1$ .

$- x + x - 4 = - 4$

$y = - \frac{x}{4} + 1$

$- x + x - 4 = - 4$

$y = - \frac{x}{4} + 1$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $- x$ and $x$ .

$0 - 4 = - 4$

$y = - \frac{x}{4} + 1$

Step 2.2.1.2.2

Subtract $4$ from $0$ .

$- 4 = - 4$

$y = - \frac{x}{4} + 1$

$- 4 = - 4$

$y = - \frac{x}{4} + 1$

$- 4 = - 4$

$y = - \frac{x}{4} + 1$

$- 4 = - 4$

$y = - \frac{x}{4} + 1$

$- 4 = - 4$

$y = - \frac{x}{4} + 1$

Step 3

Remove any equations from the system that are always true.

$y = - \frac{x}{4} + 1$

Step 4