Finite Math Examples

$x = 8 y + 4$ , $x = 9 y + 8$

Step 1

Eliminate the equal sides of each equation and combine.

$8 y + 4 = 9 y + 8$

Step 2

Solve $8 y + 4 = 9 y + 8$ for $y$ .

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Step 2.1

Move all terms containing $y$ to the left side of the equation.

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Step 2.1.1

Subtract $9 y$ from both sides of the equation.

$8 y + 4 - 9 y = 8$

Step 2.1.2

Subtract $9 y$ from $8 y$ .

$- y + 4 = 8$

Step 2.2

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

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Step 2.2.1

Subtract $4$ from both sides of the equation.

$- y = 8 - 4$

Step 2.2.2

Subtract $4$ from $8$ .

$- y = 4$

Step 2.3

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

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Step 2.3.1

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

$\frac{- y}{- 1} = \frac{4}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{4}{- 1}$

Step 2.3.2.2

Divide $y$ by $1$ .

$y = \frac{4}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $4$ by $- 1$ .

$y = - 4$

Step 3

Evaluate $x$ when $y = - 4$ .

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Step 3.1

Substitute $- 4$ for $y$ .

$x = 9 (- 4) + 8$

Step 3.2

Simplify $9 (- 4) + 8$ .

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Step 3.2.1

Multiply $9$ by $- 4$ .

$x = - 36 + 8$

Step 3.2.2

Add $- 36$ and $8$ .

$x = - 28$

Step 4

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

$(- 28, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(- 28, - 4)$

Equation Form:

$x = - 28, y = - 4$

Step 6