Finite Math Examples

$8 y - x = - 32$ , $x - y = - 6$

Step 1

Add $y$ to both sides of the equation.

$x = - 6 + y$

$8 y - x = - 32$

Step 2

Replace all occurrences of $x$ with $- 6 + y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $8 y - x = - 32$ with $- 6 + y$ .

$8 y - (- 6 + y) = - 32$

$x = - 6 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $8 y - (- 6 + y)$ .

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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.

$8 y + 6 - y = - 32$

$x = - 6 + y$

Step 2.2.1.1.2

Multiply $- 1$ by $- 6$ .

$8 y + 6 - y = - 32$

$x = - 6 + y$

$8 y + 6 - y = - 32$

$x = - 6 + y$

Step 2.2.1.2

Subtract $y$ from $8 y$ .

$7 y + 6 = - 32$

$x = - 6 + y$

$7 y + 6 = - 32$

$x = - 6 + y$

$7 y + 6 = - 32$

$x = - 6 + y$

$7 y + 6 = - 32$

$x = - 6 + y$

Step 3

Solve for $y$ in $7 y + 6 = - 32$ .

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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

Subtract $6$ from both sides of the equation.

$7 y = - 32 - 6$

$x = - 6 + y$

Step 3.1.2

Subtract $6$ from $- 32$ .

$7 y = - 38$

$x = - 6 + y$

$7 y = - 38$

$x = - 6 + y$

Step 3.2

Divide each term in $7 y = - 38$ by $7$ and simplify.

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Step 3.2.1

Divide each term in $7 y = - 38$ by $7$ .

$\frac{7 y}{7} = \frac{- 38}{7}$

$x = - 6 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $7$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 38}{7}$

$x = - 6 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 38}{7}$

$x = - 6 + y$

$y = \frac{- 38}{7}$

$x = - 6 + y$

$y = \frac{- 38}{7}$

$x = - 6 + y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$y = - \frac{38}{7}$

$x = - 6 + y$

$y = - \frac{38}{7}$

$x = - 6 + y$

$y = - \frac{38}{7}$

$x = - 6 + y$

$y = - \frac{38}{7}$

$x = - 6 + y$

Step 4

Replace all occurrences of $y$ with $- \frac{38}{7}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 6 + y$ with $- \frac{38}{7}$ .

$x = - 6 - \frac{38}{7}$

$y = - \frac{38}{7}$

Step 4.2

Simplify $x = - 6 - \frac{38}{7}$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 6 - \frac{38}{7}$

$y = - \frac{38}{7}$

$x = - 6 - \frac{38}{7}$

$y = - \frac{38}{7}$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify $- 6 - \frac{38}{7}$ .

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Step 4.2.2.1.1

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = - 6 \cdot \frac{7}{7} - \frac{38}{7}$

$y = - \frac{38}{7}$

Step 4.2.2.1.2

Combine $- 6$ and $\frac{7}{7}$ .

$x = \frac{- 6 \cdot 7}{7} - \frac{38}{7}$

$y = - \frac{38}{7}$

Step 4.2.2.1.3

Combine the numerators over the common denominator.

$x = \frac{- 6 \cdot 7 - 38}{7}$

$y = - \frac{38}{7}$

Step 4.2.2.1.4

Simplify the numerator.

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Step 4.2.2.1.4.1

Multiply $- 6$ by $7$ .

$x = \frac{- 42 - 38}{7}$

$y = - \frac{38}{7}$

Step 4.2.2.1.4.2

Subtract $38$ from $- 42$ .

$x = \frac{- 80}{7}$

$y = - \frac{38}{7}$

$x = \frac{- 80}{7}$

$y = - \frac{38}{7}$

Step 4.2.2.1.5

Move the negative in front of the fraction.

$x = - \frac{80}{7}$

$y = - \frac{38}{7}$

$x = - \frac{80}{7}$

$y = - \frac{38}{7}$

$x = - \frac{80}{7}$

$y = - \frac{38}{7}$

$x = - \frac{80}{7}$

$y = - \frac{38}{7}$

$x = - \frac{80}{7}$

$y = - \frac{38}{7}$

Step 5

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

$(- \frac{80}{7}, - \frac{38}{7})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{80}{7}, - \frac{38}{7})$

Equation Form:

$x = - \frac{80}{7}, y = - \frac{38}{7}$

Step 7