Finite Math Examples

$- 5 x + 4 = 6$ , $6 x + 8 y = - 84$

Step 1

Solve for $x$ in $- 5 x + 4 = 6$ .

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Step 1.1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1.1

Subtract $4$ from both sides of the equation.

$- 5 x = 6 - 4$

$6 x + 8 y = - 84$

Step 1.1.2

Subtract $4$ from $6$ .

$- 5 x = 2$

$6 x + 8 y = - 84$

$- 5 x = 2$

$6 x + 8 y = - 84$

Step 1.2

Divide each term in $- 5 x = 2$ by $- 5$ and simplify.

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Step 1.2.1

Divide each term in $- 5 x = 2$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{2}{- 5}$

$6 x + 8 y = - 84$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{2}{- 5}$

$6 x + 8 y = - 84$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{- 5}$

$6 x + 8 y = - 84$

$x = \frac{2}{- 5}$

$6 x + 8 y = - 84$

$x = \frac{2}{- 5}$

$6 x + 8 y = - 84$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$x = - \frac{2}{5}$

$6 x + 8 y = - 84$

$x = - \frac{2}{5}$

$6 x + 8 y = - 84$

$x = - \frac{2}{5}$

$6 x + 8 y = - 84$

$x = - \frac{2}{5}$

$6 x + 8 y = - 84$

Step 2

Replace all occurrences of $x$ with $- \frac{2}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $6 x + 8 y = - 84$ with $- \frac{2}{5}$ .

$6 (- \frac{2}{5}) + 8 y = - 84$

$x = - \frac{2}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $6 (- \frac{2}{5})$ .

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Step 2.2.1.1.1

Multiply $- 1$ by $6$ .

$- 6 (\frac{2}{5}) + 8 y = - 84$

$x = - \frac{2}{5}$

Step 2.2.1.1.2

Combine $- 6$ and $\frac{2}{5}$ .

$\frac{- 6 \cdot 2}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

Step 2.2.1.1.3

Multiply $- 6$ by $2$ .

$\frac{- 12}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

$\frac{- 12}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

Step 2.2.1.2

Move the negative in front of the fraction.

$- \frac{12}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

$- \frac{12}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

$- \frac{12}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

$- \frac{12}{5} + 8 y = - 84$

$x = - \frac{2}{5}$

Step 3

Solve for $y$ in $- \frac{12}{5} + 8 y = - 84$ .

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Step 3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1.1

Add $\frac{12}{5}$ to both sides of the equation.

$8 y = - 84 + \frac{12}{5}$

$x = - \frac{2}{5}$

Step 3.1.2

To write $- 84$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$8 y = - 84 \cdot \frac{5}{5} + \frac{12}{5}$

$x = - \frac{2}{5}$

Step 3.1.3

Combine $- 84$ and $\frac{5}{5}$ .

$8 y = \frac{- 84 \cdot 5}{5} + \frac{12}{5}$

$x = - \frac{2}{5}$

Step 3.1.4

Combine the numerators over the common denominator.

$8 y = \frac{- 84 \cdot 5 + 12}{5}$

$x = - \frac{2}{5}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $- 84$ by $5$ .

$8 y = \frac{- 420 + 12}{5}$

$x = - \frac{2}{5}$

Step 3.1.5.2

Add $- 420$ and $12$ .

$8 y = \frac{- 408}{5}$

$x = - \frac{2}{5}$

$8 y = \frac{- 408}{5}$

$x = - \frac{2}{5}$

Step 3.1.6

Move the negative in front of the fraction.

$8 y = - \frac{408}{5}$

$x = - \frac{2}{5}$

$8 y = - \frac{408}{5}$

$x = - \frac{2}{5}$

Step 3.2

Divide each term in $8 y = - \frac{408}{5}$ by $8$ and simplify.

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Step 3.2.1

Divide each term in $8 y = - \frac{408}{5}$ by $8$ .

$\frac{8 y}{8} = \frac{- \frac{408}{5}}{8}$

$x = - \frac{2}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- \frac{408}{5}}{8}$

$x = - \frac{2}{5}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{408}{5}}{8}$

$x = - \frac{2}{5}$

$y = \frac{- \frac{408}{5}}{8}$

$x = - \frac{2}{5}$

$y = \frac{- \frac{408}{5}}{8}$

$x = - \frac{2}{5}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{408}{5} \cdot \frac{1}{8}$

$x = - \frac{2}{5}$

Step 3.2.3.2

Cancel the common factor of $8$ .

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Step 3.2.3.2.1

Move the leading negative in $- \frac{408}{5}$ into the numerator.

$y = \frac{- 408}{5} \cdot \frac{1}{8}$

$x = - \frac{2}{5}$

Step 3.2.3.2.2

Factor $8$ out of $- 408$ .

$y = \frac{8 (- 51)}{5} \cdot \frac{1}{8}$

$x = - \frac{2}{5}$

Step 3.2.3.2.3

Cancel the common factor.

$y = \frac{8 \cdot - 51}{5} \cdot \frac{1}{8}$

$x = - \frac{2}{5}$

Step 3.2.3.2.4

Rewrite the expression.

$y = \frac{- 51}{5}$

$x = - \frac{2}{5}$

$y = \frac{- 51}{5}$

$x = - \frac{2}{5}$

Step 3.2.3.3

Move the negative in front of the fraction.

$y = - \frac{51}{5}$

$x = - \frac{2}{5}$

$y = - \frac{51}{5}$

$x = - \frac{2}{5}$

$y = - \frac{51}{5}$

$x = - \frac{2}{5}$

$y = - \frac{51}{5}$

$x = - \frac{2}{5}$

Step 4

Solve the system of equations.

$y = - \frac{51}{5} x = - \frac{2}{5}$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- \frac{2}{5}, - \frac{51}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{2}{5}, - \frac{51}{5})$

Equation Form:

$x = - \frac{2}{5}, y = - \frac{51}{5}$

Step 7