Finite Math Examples

$y = - 2 x + 180$ , $y = 100 - \frac{1 x}{3}$

Step 1

Eliminate the equal sides of each equation and combine.

$- 2 x + 180 = 100 - \frac{x}{3}$

Step 2

Solve $- 2 x + 180 = 100 - \frac{x}{3}$ for $x$ .

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Step 2.1

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

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Step 2.1.1

Add $\frac{x}{3}$ to both sides of the equation.

$- 2 x + 180 + \frac{x}{3} = 100$

Step 2.1.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 2 x \cdot \frac{3}{3} + \frac{x}{3} + 180 = 100$

Step 2.1.3

Combine $- 2 x$ and $\frac{3}{3}$ .

$\frac{- 2 x \cdot 3}{3} + \frac{x}{3} + 180 = 100$

Step 2.1.4

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 3 + x}{3} + 180 = 100$

Step 2.1.5

Simplify each term.

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Step 2.1.5.1

Simplify the numerator.

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Step 2.1.5.1.1

Factor $x$ out of $- 2 x \cdot 3 + x$ .

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Step 2.1.5.1.1.1

Factor $x$ out of $- 2 x \cdot 3$ .

$\frac{x (- 2 \cdot 3) + x}{3} + 180 = 100$

Step 2.1.5.1.1.2

Raise $x$ to the power of $1$ .

$\frac{x (- 2 \cdot 3) + x^{1}}{3} + 180 = 100$

Step 2.1.5.1.1.3

Factor $x$ out of $x^{1}$ .

$\frac{x (- 2 \cdot 3) + x \cdot 1}{3} + 180 = 100$

Step 2.1.5.1.1.4

Factor $x$ out of $x (- 2 \cdot 3) + x \cdot 1$ .

$\frac{x (- 2 \cdot 3 + 1)}{3} + 180 = 100$

Step 2.1.5.1.2

Multiply $- 2$ by $3$ .

$\frac{x (- 6 + 1)}{3} + 180 = 100$

Step 2.1.5.1.3

Add $- 6$ and $1$ .

$\frac{x \cdot - 5}{3} + 180 = 100$

Step 2.1.5.2

Move $- 5$ to the left of $x$ .

$\frac{- 5 \cdot x}{3} + 180 = 100$

Step 2.1.5.3

Move the negative in front of the fraction.

$- \frac{5 x}{3} + 180 = 100$

Step 2.2

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

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Step 2.2.1

Subtract $180$ from both sides of the equation.

$- \frac{5 x}{3} = 100 - 180$

Step 2.2.2

Subtract $180$ from $100$ .

$- \frac{5 x}{3} = - 80$

Step 2.3

Multiply both sides of the equation by $- \frac{3}{5}$ .

$- \frac{3}{5} (- \frac{5 x}{3}) = - \frac{3}{5} \cdot - 80$

Step 2.4

Simplify both sides of the equation.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Simplify $- \frac{3}{5} (- \frac{5 x}{3})$ .

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Step 2.4.1.1.1

Cancel the common factor of $3$ .

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Step 2.4.1.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{- 3}{5} (- \frac{5 x}{3}) = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.1.2

Move the leading negative in $- \frac{5 x}{3}$ into the numerator.

$\frac{- 3}{5} \cdot \frac{- 5 x}{3} = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{5} \cdot \frac{- 5 x}{3} = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{5} \cdot \frac{- 5 x}{3} = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 x) = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.2

Cancel the common factor of $5$ .

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Step 2.4.1.1.2.1

Factor $5$ out of $- 5 x$ .

$\frac{- 1}{5} (5 (- x)) = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- x)) = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.3

Multiply.

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Step 2.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{5} \cdot - 80$

Step 2.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{5} \cdot - 80$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Simplify $- \frac{3}{5} \cdot - 80$ .

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Step 2.4.2.1.1

Cancel the common factor of $5$ .

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Step 2.4.2.1.1.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$x = \frac{- 3}{5} \cdot - 80$

Step 2.4.2.1.1.2

Factor $5$ out of $- 80$ .

$x = \frac{- 3}{5} \cdot (5 (- 16))$

Step 2.4.2.1.1.3

Cancel the common factor.

$x = \frac{- 3}{5} \cdot (5 \cdot - 16)$

Step 2.4.2.1.1.4

Rewrite the expression.

$x = - 3 \cdot - 16$

Step 2.4.2.1.2

Multiply $- 3$ by $- 16$ .

$x = 48$

Step 3

Evaluate $y$ when $x = 48$ .

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Step 3.1

Substitute $48$ for $x$ .

$y = 100 - \frac{48}{3}$

Step 3.2

Substitute $48$ for $x$ in $y = 100 - \frac{48}{3}$ and solve for $y$ .

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Step 3.2.1

Remove parentheses.

$y = 100 - \frac{48}{3}$

Step 3.2.2

Simplify $100 - \frac{48}{3}$ .

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Step 3.2.2.1

Simplify each term.

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Step 3.2.2.1.1

Divide $48$ by $3$ .

$y = 100 - 1 \cdot 16$

Step 3.2.2.1.2

Multiply $- 1$ by $16$ .

$y = 100 - 16$

Step 3.2.2.2

Subtract $16$ from $100$ .

$y = 84$

Step 4

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

$(48, 84)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(48, 84)$

Equation Form:

$x = 48, y = 84$

Step 6