Finite Math Examples

$4 x + 12 y = 12$ , $5 x + 15 y = 15$

Step 1

Solve for $x$ in $4 x + 12 y = 12$ .

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Step 1.1

Subtract $12 y$ from both sides of the equation.

$4 x = 12 - 12 y$

$5 x + 15 y = 15$

Step 1.2

Divide each term in $4 x = 12 - 12 y$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x = 12 - 12 y$ by $4$ .

$\frac{4 x}{4} = \frac{12}{4} + \frac{- 12 y}{4}$

$5 x + 15 y = 15$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{12}{4} + \frac{- 12 y}{4}$

$5 x + 15 y = 15$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{4} + \frac{- 12 y}{4}$

$5 x + 15 y = 15$

$x = \frac{12}{4} + \frac{- 12 y}{4}$

$5 x + 15 y = 15$

$x = \frac{12}{4} + \frac{- 12 y}{4}$

$5 x + 15 y = 15$

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 $12$ by $4$ .

$x = 3 + \frac{- 12 y}{4}$

$5 x + 15 y = 15$

Step 1.2.3.1.2

Cancel the common factor of $- 12$ and $4$ .

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Step 1.2.3.1.2.1

Factor $4$ out of $- 12 y$ .

$x = 3 + \frac{4 (- 3 y)}{4}$

$5 x + 15 y = 15$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $4$ out of $4$ .

$x = 3 + \frac{4 (- 3 y)}{4 (1)}$

$5 x + 15 y = 15$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = 3 + \frac{4 (- 3 y)}{4 \cdot 1}$

$5 x + 15 y = 15$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = 3 + \frac{- 3 y}{1}$

$5 x + 15 y = 15$

Step 1.2.3.1.2.2.4

Divide $- 3 y$ by $1$ .

$x = 3 - 3 y$

$5 x + 15 y = 15$

$x = 3 - 3 y$

$5 x + 15 y = 15$

$x = 3 - 3 y$

$5 x + 15 y = 15$

$x = 3 - 3 y$

$5 x + 15 y = 15$

$x = 3 - 3 y$

$5 x + 15 y = 15$

$x = 3 - 3 y$

$5 x + 15 y = 15$

$x = 3 - 3 y$

$5 x + 15 y = 15$

Step 2

Replace all occurrences of $x$ with $3 - 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $5 x + 15 y = 15$ with $3 - 3 y$ .

$5 (3 - 3 y) + 15 y = 15$

$x = 3 - 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $5 (3 - 3 y) + 15 y$ .

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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.

$5 \cdot 3 + 5 (- 3 y) + 15 y = 15$

$x = 3 - 3 y$

Step 2.2.1.1.2

Multiply $5$ by $3$ .

$15 + 5 (- 3 y) + 15 y = 15$

$x = 3 - 3 y$

Step 2.2.1.1.3

Multiply $- 3$ by $5$ .

$15 - 15 y + 15 y = 15$

$x = 3 - 3 y$

$15 - 15 y + 15 y = 15$

$x = 3 - 3 y$

Step 2.2.1.2

Combine the opposite terms in $15 - 15 y + 15 y$ .

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Step 2.2.1.2.1

Add $- 15 y$ and $15 y$ .

$15 + 0 = 15$

$x = 3 - 3 y$

Step 2.2.1.2.2

Add $15$ and $0$ .

$15 = 15$

$x = 3 - 3 y$

$15 = 15$

$x = 3 - 3 y$

$15 = 15$

$x = 3 - 3 y$

$15 = 15$

$x = 3 - 3 y$

$15 = 15$

$x = 3 - 3 y$

Step 3

Remove any equations from the system that are always true.

$x = 3 - 3 y$

Step 4