Finite Math Examples

$0.5 x + y = 20000000$ , $x = 5000000$ , $y = 10000000$ , $x + y = 25000000$

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 $0.5 x$ from both sides of the equation.

$y = 20000000 - 0.5 x$

Step 1.3

Reorder $20000000$ and $- 0.5 x$ .

$y = - 0.5 x + 20000000$

Step 2

Using the slope-intercept form, the slope is $- 0.5$ .

$m_{1} = - 0.5$

Step 3

Since $x = 5000000$ 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.

$y = 25000000 - x$

Step 5.3

Reorder $25000000$ and $- x$ .

$y = - x + 25000000$

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.

$0.5 x + y = 20000000, x = 5000000, y = 10000000, x + y = 25000000$

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 $5000000$ in each equation.

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Step 8.1.1

Replace all occurrences of $x$ in $0.5 x + y = 20000000$ with $5000000$ .

$0.5 (5000000) + y = 20000000$

$x = 5000000$

$y = 10000000$

$x + y = 25000000$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Multiply $0.5$ by $5000000$ .

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

$x + y = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

$x + y = 25000000$

Step 8.1.3

Replace all occurrences of $x$ in $x + y = 25000000$ with $5000000$ .

$(5000000) + y = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

Step 8.1.4

Simplify the left side.

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Step 8.1.4.1

Remove parentheses.

$5000000 + y = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

$5000000 + y = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

$5000000 + y = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

Step 8.2

Replace all occurrences of $y$ with $10000000$ in each equation.

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Step 8.2.1

Replace all occurrences of $y$ in $5000000 + y = 25000000$ with $10000000$ .

$5000000 + 10000000 = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Simplify $5000000 + 10000000$ .

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Step 8.2.2.1.1

Remove parentheses.

$5000000 + 10000000 = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

Step 8.2.2.1.2

Add $5000000$ and $10000000$ .

$15000000 = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

$15000000 = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

$15000000 = 25000000$

$2500000 + y = 20000000$

$x = 5000000$

$y = 10000000$

Step 8.2.3

Replace all occurrences of $y$ in $2500000 + y = 20000000$ with $10000000$ .

$2500000 + 10000000 = 20000000$

$15000000 = 25000000$

$x = 5000000$

$y = 10000000$

Step 8.2.4

Simplify the left side.

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Step 8.2.4.1

Simplify $2500000 + 10000000$ .

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Step 8.2.4.1.1

Remove parentheses.

$2500000 + 10000000 = 20000000$

$15000000 = 25000000$

$x = 5000000$

$y = 10000000$

Step 8.2.4.1.2

Add $2500000$ and $10000000$ .

$12500000 = 20000000$

$15000000 = 25000000$

$x = 5000000$

$y = 10000000$

$12500000 = 20000000$

$15000000 = 25000000$

$x = 5000000$

$y = 10000000$

$12500000 = 20000000$

$15000000 = 25000000$

$x = 5000000$

$y = 10000000$

$12500000 = 20000000$

$15000000 = 25000000$

$x = 5000000$

$y = 10000000$

Step 8.3

Since $12500000 = 20000000$ 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