Finite Math Examples

$2.4 x + 0.08 y = 144$ , $x = 55$ , $y = 90$ , $x + y = 100$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Subtract $2.4 x$ from both sides of the equation.

$0.08 y = 144 - 2.4 x$

Step 1.3

Divide each term in $0.08 y = 144 - 2.4 x$ by $0.08$ and simplify.

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Step 1.3.1

Divide each term in $0.08 y = 144 - 2.4 x$ by $0.08$ .

$\frac{0.08 y}{0.08} = \frac{144}{0.08} + \frac{- 2.4 x}{0.08}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $0.08$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{0.08 y}{0.08} = \frac{144}{0.08} + \frac{- 2.4 x}{0.08}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{144}{0.08} + \frac{- 2.4 x}{0.08}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide $144$ by $0.08$ .

$y = 1800 + \frac{- 2.4 x}{0.08}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = 1800 - \frac{2.4 x}{0.08}$

Step 1.3.3.1.3

Factor $2.4$ out of $2.4 x$ .

$y = 1800 - \frac{2.4 (x)}{0.08}$

Step 1.3.3.1.4

Factor $0.08$ out of $0.08$ .

$y = 1800 - \frac{2.4 (x)}{0.08 (1)}$

Step 1.3.3.1.5

Separate fractions.

$y = 1800 - (\frac{2.4}{0.08} \cdot \frac{x}{1})$

Step 1.3.3.1.6

Divide $2.4$ by $0.08$ .

$y = 1800 - (30 \frac{x}{1})$

Step 1.3.3.1.7

Divide $x$ by $1$ .

$y = 1800 - (30 x)$

Step 1.3.3.1.8

Multiply $30$ by $- 1$ .

$y = 1800 - 30 x$

Step 1.4

Reorder $1800$ and $- 30 x$ .

$y = - 30 x + 1800$

Step 2

Using the slope-intercept form, the slope is $- 30$ .

$m_{1} = - 30$

Step 3

Since $x = 55$ is a vertical line, the slope is undefined.

Undefined

Step 4

Use the slope-intercept form to find the slope.

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Step 4.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 4.2

Using the slope-intercept form, the slope is $0$ .

$m_{3} = 0$

Step 5

Rewrite in slope-intercept form.

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Step 5.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 5.2

Subtract $x$ from both sides of the equation.

$y = 100 - x$

Step 5.3

Reorder $100$ and $- x$ .

$y = - x + 100$

Step 6

Using the slope-intercept form, the slope is $- 1$ .

$m_{4} = - 1$

Step 7

Set up the system of equations to find any points of intersection.

$2.4 x + 0.08 y = 144, x = 55, y = 90, x + y = 100$

Step 8

Solve the system of equations to find the point of intersection.

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Step 8.1

Replace all occurrences of $x$ with $55$ in each equation.

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Step 8.1.1

Replace all occurrences of $x$ in $2.4 x + 0.08 y = 144$ with $55$ .

$2.4 (55) + 0.08 y = 144$

$x = 55$

$y = 90$

$x + y = 100$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Multiply $2.4$ by $55$ .

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

$x + y = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

$x + y = 100$

Step 8.1.3

Replace all occurrences of $x$ in $x + y = 100$ with $55$ .

$(55) + y = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

Step 8.1.4

Simplify the left side.

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Step 8.1.4.1

Remove parentheses.

$55 + y = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

$55 + y = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

$55 + y = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

Step 8.2

Replace all occurrences of $y$ with $90$ in each equation.

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Step 8.2.1

Replace all occurrences of $y$ in $55 + y = 100$ with $90$ .

$55 + 90 = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Simplify $55 + 90$ .

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Step 8.2.2.1.1

Remove parentheses.

$55 + 90 = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

Step 8.2.2.1.2

Add $55$ and $90$ .

$145 = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

$145 = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

$145 = 100$

$132 + 0.08 y = 144$

$x = 55$

$y = 90$

Step 8.2.3

Replace all occurrences of $y$ in $132 + 0.08 y = 144$ with $90$ .

$132 + 0.08 (90) = 144$

$145 = 100$

$x = 55$

$y = 90$

Step 8.2.4

Simplify the left side.

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Step 8.2.4.1

Simplify $132 + 0.08 (90)$ .

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Step 8.2.4.1.1

Multiply $0.08$ by $90$ .

$132 + 7.2 = 144$

$145 = 100$

$x = 55$

$y = 90$

Step 8.2.4.1.2

Add $132$ and $7.2$ .

$139.2 = 144$

$145 = 100$

$x = 55$

$y = 90$

$139.2 = 144$

$145 = 100$

$x = 55$

$y = 90$

$139.2 = 144$

$145 = 100$

$x = 55$

$y = 90$

$139.2 = 144$

$145 = 100$

$x = 55$

$y = 90$

Step 8.3

Since $139.2 = 144$ is not true, there is no solution.

No solution

Step 9

Since the slopes are different, the lines will have exactly one intersection point.

No solution

Step 10