Finite Math Examples

$6 x + 4 y = - 12$ , $- 3 x - 2 y = 6$

Step 1

Solve for $x$ in $6 x + 4 y = - 12$ .

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Step 1.1

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

$6 x = - 12 - 4 y$

$- 3 x - 2 y = 6$

Step 1.2

Divide each term in $6 x = - 12 - 4 y$ by $6$ and simplify.

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Step 1.2.1

Divide each term in $6 x = - 12 - 4 y$ by $6$ .

$\frac{6 x}{6} = \frac{- 12}{6} + \frac{- 4 y}{6}$

$- 3 x - 2 y = 6$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $6$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 12}{6} + \frac{- 4 y}{6}$

$- 3 x - 2 y = 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{6} + \frac{- 4 y}{6}$

$- 3 x - 2 y = 6$

$x = \frac{- 12}{6} + \frac{- 4 y}{6}$

$- 3 x - 2 y = 6$

$x = \frac{- 12}{6} + \frac{- 4 y}{6}$

$- 3 x - 2 y = 6$

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 $6$ .

$x = - 2 + \frac{- 4 y}{6}$

$- 3 x - 2 y = 6$

Step 1.2.3.1.2

Cancel the common factor of $- 4$ and $6$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $- 4 y$ .

$x = - 2 + \frac{2 (- 2 y)}{6}$

$- 3 x - 2 y = 6$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $6$ .

$x = - 2 + \frac{2 (- 2 y)}{2 (3)}$

$- 3 x - 2 y = 6$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = - 2 + \frac{2 (- 2 y)}{2 \cdot 3}$

$- 3 x - 2 y = 6$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = - 2 + \frac{- 2 y}{3}$

$- 3 x - 2 y = 6$

$x = - 2 + \frac{- 2 y}{3}$

$- 3 x - 2 y = 6$

$x = - 2 + \frac{- 2 y}{3}$

$- 3 x - 2 y = 6$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x = - 2 - \frac{2 y}{3}$

$- 3 x - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

$- 3 x - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

$- 3 x - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

$- 3 x - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

$- 3 x - 2 y = 6$

Step 2

Replace all occurrences of $x$ with $- 2 - \frac{2 y}{3}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 3 x - 2 y = 6$ with $- 2 - \frac{2 y}{3}$ .

$- 3 (- 2 - \frac{2 y}{3}) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 (- 2 - \frac{2 y}{3}) - 2 y$ .

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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.

$- 3 \cdot - 2 - 3 (- \frac{2 y}{3}) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.1.2

Multiply $- 3$ by $- 2$ .

$6 - 3 (- \frac{2 y}{3}) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.1.3

Cancel the common factor of $3$ .

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Step 2.2.1.1.3.1

Move the leading negative in $- \frac{2 y}{3}$ into the numerator.

$6 - 3 \frac{- 2 y}{3} - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.1.3.2

Factor $3$ out of $- 3$ .

$6 + 3 (- 1) (\frac{- 2 y}{3}) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.1.3.3

Cancel the common factor.

$6 + 3 \cdot (- 1 \frac{- 2 y}{3}) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.1.3.4

Rewrite the expression.

$6 - 1 (- 2 y) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

$6 - 1 (- 2 y) - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.1.4

Multiply $- 2$ by $- 1$ .

$6 + 2 y - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

$6 + 2 y - 2 y = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.2

Combine the opposite terms in $6 + 2 y - 2 y$ .

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Step 2.2.1.2.1

Subtract $2 y$ from $2 y$ .

$6 + 0 = 6$

$x = - 2 - \frac{2 y}{3}$

Step 2.2.1.2.2

Add $6$ and $0$ .

$6 = 6$

$x = - 2 - \frac{2 y}{3}$

$6 = 6$

$x = - 2 - \frac{2 y}{3}$

$6 = 6$

$x = - 2 - \frac{2 y}{3}$

$6 = 6$

$x = - 2 - \frac{2 y}{3}$

$6 = 6$

$x = - 2 - \frac{2 y}{3}$

Step 3

Remove any equations from the system that are always true.

$x = - 2 - \frac{2 y}{3}$

Step 4