Finite Math Examples

y - x = 8

$y - x = 8$ ,

x - y = 2

$x - y = 2$

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

Add

x

$x$ to both sides of the equation.

y = 8 + x

$y = 8 + x$

Step 1.3

Reorder

8

$8$ and

x

$x$ .

y = x + 8

$y = x + 8$

y = x + 8

$y = x + 8$

Step 2

Using the slope-intercept form, the slope is

1

$1$ .

m_{1} = 1

$m_{1} = 1$

Step 3

Rewrite in slope-intercept form.

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Step 3.1

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 3.2

Subtract

x

$x$ from both sides of the equation.

- y = 2 - x

$- y = 2 - x$

Step 3.3

Divide each term in

- y = 2 - x

$- y = 2 - x$ by

- 1

$- 1$ and simplify.

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Step 3.3.1

Divide each term in

- y = 2 - x

$- y = 2 - x$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{2}{- 1} + \frac{- x}{- 1}

$\frac{- y}{- 1} = \frac{2}{- 1} + \frac{- x}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} = \frac{2}{- 1} + \frac{- x}{- 1}

$\frac{y}{1} = \frac{2}{- 1} + \frac{- x}{- 1}$

Step 3.3.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{2}{- 1} + \frac{- x}{- 1}

$y = \frac{2}{- 1} + \frac{- x}{- 1}$

y = \frac{2}{- 1} + \frac{- x}{- 1}

$y = \frac{2}{- 1} + \frac{- x}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Simplify each term.

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Step 3.3.3.1.1

Divide

2

$2$ by

- 1

$- 1$ .

y = - 2 + \frac{- x}{- 1}

$y = - 2 + \frac{- x}{- 1}$

Step 3.3.3.1.2

Dividing two negative values results in a positive value.

y = - 2 + \frac{x}{1}

$y = - 2 + \frac{x}{1}$

Step 3.3.3.1.3

Divide

x

$x$ by

1

$1$ .

y = - 2 + x

$y = - 2 + x$

y = - 2 + x

$y = - 2 + x$

y = - 2 + x

$y = - 2 + x$

y = - 2 + x

$y = - 2 + x$

Step 3.4

Reorder

- 2

$- 2$ and

x

$x$ .

y = x - 2

$y = x - 2$

y = x - 2

$y = x - 2$

Step 4

Using the slope-intercept form, the slope is

1

$1$ .

m_{2} = 1

$m_{2} = 1$

Step 5

Since the slopes are the same, the lines are parallel and do not intersect, so the system has no solutions.

m_{1} = 1

$m_{1} = 1$

m_{2} = 1

$m_{2} = 1$

Step 6