Finite Math Examples

0.5 x + y = 20000000

$0.5 x + y = 20000000$ ,

x = 5000000

$x = 5000000$ ,

y = 10000000

$y = 10000000$ ,

x + y = 25000000

$x + y = 25000000$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Subtract

0.5 x

$0.5 x$ from both sides of the equation.

y = 20000000 - 0.5 x

$y = 20000000 - 0.5 x$

Step 1.3

Reorder

20000000

$20000000$ and

- 0.5 x

$- 0.5 x$ .

y = - 0.5 x + 20000000

$y = - 0.5 x + 20000000$

y = - 0.5 x + 20000000

$y = - 0.5 x + 20000000$

Step 2

Using the slope-intercept form, the slope is

- 0.5

$- 0.5$ .

m_{1} = - 0.5

$m_{1} = - 0.5$

Step 3

Since

x = 5000000

$x = 5000000$ 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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 4.2

Using the slope-intercept form, the slope is

0

$0$ .

m_{3} = 0

$m_{3} = 0$

m_{3} = 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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 5.2

Subtract

x

$x$ from both sides of the equation.

y = 25000000 - x

$y = 25000000 - x$

Step 5.3

Reorder

25000000

$25000000$ and

- x

$- x$ .

y = - x + 25000000

$y = - x + 25000000$

y = - x + 25000000

$y = - x + 25000000$

Step 6

Using the slope-intercept form, the slope is

- 1

$- 1$ .

m_{4} = - 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

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

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

$x$ with

5000000

$5000000$ in each equation.

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Step 8.1.1

Replace all occurrences of

x

$x$ in

0.5 x + y = 20000000

$0.5 x + y = 20000000$ with

5000000

$5000000$ .

0.5 (5000000) + y = 20000000

$0.5 (5000000) + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

x + y = 25000000

$x + y = 25000000$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Multiply

0.5

$0.5$ by

5000000

$5000000$ .

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

x + y = 25000000

$x + y = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

x + y = 25000000

$x + y = 25000000$

Step 8.1.3

Replace all occurrences of

x

$x$ in

x + y = 25000000

$x + y = 25000000$ with

5000000

$5000000$ .

(5000000) + y = 25000000

$(5000000) + y = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.1.4

Simplify the left side.

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Step 8.1.4.1

Remove parentheses.

5000000 + y = 25000000

$5000000 + y = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

5000000 + y = 25000000

$5000000 + y = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

5000000 + y = 25000000

$5000000 + y = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.2

Replace all occurrences of

y

$y$ with

10000000

$10000000$ in each equation.

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Step 8.2.1

Replace all occurrences of

y

$y$ in

5000000 + y = 25000000

$5000000 + y = 25000000$ with

10000000

$10000000$ .

5000000 + 10000000 = 25000000

$5000000 + 10000000 = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.2.2

Simplify the left side.

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Step 8.2.2.1

Simplify

5000000 + 10000000

$5000000 + 10000000$ .

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Step 8.2.2.1.1

Remove parentheses.

5000000 + 10000000 = 25000000

$5000000 + 10000000 = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.2.2.1.2

Add

5000000

$5000000$ and

10000000

$10000000$ .

15000000 = 25000000

$15000000 = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

15000000 = 25000000

$15000000 = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

15000000 = 25000000

$15000000 = 25000000$

2500000 + y = 20000000

$2500000 + y = 20000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.2.3

Replace all occurrences of

y

$y$ in

2500000 + y = 20000000

$2500000 + y = 20000000$ with

10000000

$10000000$ .

2500000 + 10000000 = 20000000

$2500000 + 10000000 = 20000000$

15000000 = 25000000

$15000000 = 25000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.2.4

Simplify the left side.

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Step 8.2.4.1

Simplify

2500000 + 10000000

$2500000 + 10000000$ .

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Step 8.2.4.1.1

Remove parentheses.

2500000 + 10000000 = 20000000

$2500000 + 10000000 = 20000000$

15000000 = 25000000

$15000000 = 25000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.2.4.1.2

Add

2500000

$2500000$ and

10000000

$10000000$ .

12500000 = 20000000

$12500000 = 20000000$

15000000 = 25000000

$15000000 = 25000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

12500000 = 20000000

$12500000 = 20000000$

15000000 = 25000000

$15000000 = 25000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

12500000 = 20000000

$12500000 = 20000000$

15000000 = 25000000

$15000000 = 25000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

12500000 = 20000000

$12500000 = 20000000$

15000000 = 25000000

$15000000 = 25000000$

x = 5000000

$x = 5000000$

y = 10000000

$y = 10000000$

Step 8.3

Since

12500000 = 20000000

$12500000 = 20000000$ 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