Finite Math Examples

$- x + 4 y = 8$ , $- 3 x + 12 y = 24$

Step 1

Solve for $x$ in $- x + 4 y = 8$ .

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Step 1.1

Subtract $4 y$ from both sides of the equation.

$- x = 8 - 4 y$

$- 3 x + 12 y = 24$

Step 1.2

Divide each term in $- x = 8 - 4 y$ by $- 1$ and simplify.

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Step 1.2.1

Divide each term in $- x = 8 - 4 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{8}{- 1} + \frac{- 4 y}{- 1}$

$- 3 x + 12 y = 24$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{8}{- 1} + \frac{- 4 y}{- 1}$

$- 3 x + 12 y = 24$

Step 1.2.2.2

Divide $x$ by $1$ .

$x = \frac{8}{- 1} + \frac{- 4 y}{- 1}$

$- 3 x + 12 y = 24$

$x = \frac{8}{- 1} + \frac{- 4 y}{- 1}$

$- 3 x + 12 y = 24$

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

Divide $8$ by $- 1$ .

$x = - 8 + \frac{- 4 y}{- 1}$

$- 3 x + 12 y = 24$

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{- 4 y}{- 1}$ .

$x = - 8 - 1 \cdot (- 4 y)$

$- 3 x + 12 y = 24$

Step 1.2.3.1.3

Rewrite $- 1 \cdot (- 4 y)$ as $- (- 4 y)$ .

$x = - 8 - (- 4 y)$

$- 3 x + 12 y = 24$

Step 1.2.3.1.4

Multiply $- 4$ by $- 1$ .

$x = - 8 + 4 y$

$- 3 x + 12 y = 24$

$x = - 8 + 4 y$

$- 3 x + 12 y = 24$

$x = - 8 + 4 y$

$- 3 x + 12 y = 24$

$x = - 8 + 4 y$

$- 3 x + 12 y = 24$

$x = - 8 + 4 y$

$- 3 x + 12 y = 24$

Step 2

Replace all occurrences of $x$ with $- 8 + 4 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 3 x + 12 y = 24$ with $- 8 + 4 y$ .

$- 3 (- 8 + 4 y) + 12 y = 24$

$x = - 8 + 4 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 (- 8 + 4 y) + 12 y$ .

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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.

$- 3 \cdot - 8 - 3 (4 y) + 12 y = 24$

$x = - 8 + 4 y$

Step 2.2.1.1.2

Multiply $- 3$ by $- 8$ .

$24 - 3 (4 y) + 12 y = 24$

$x = - 8 + 4 y$

Step 2.2.1.1.3

Multiply $4$ by $- 3$ .

$24 - 12 y + 12 y = 24$

$x = - 8 + 4 y$

$24 - 12 y + 12 y = 24$

$x = - 8 + 4 y$

Step 2.2.1.2

Combine the opposite terms in $24 - 12 y + 12 y$ .

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Step 2.2.1.2.1

Add $- 12 y$ and $12 y$ .

$24 + 0 = 24$

$x = - 8 + 4 y$

Step 2.2.1.2.2

Add $24$ and $0$ .

$24 = 24$

$x = - 8 + 4 y$

$24 = 24$

$x = - 8 + 4 y$

$24 = 24$

$x = - 8 + 4 y$

$24 = 24$

$x = - 8 + 4 y$

$24 = 24$

$x = - 8 + 4 y$

Step 3

Remove any equations from the system that are always true.

$x = - 8 + 4 y$

Step 4