Finite Math Examples

$y - x = 8$ , $x - y = 2$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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

$y = m x + b$

Step 1.2

Add $x$ to both sides of the equation.

$y = 8 + x$

Step 1.3

Reorder $8$ and $x$ .

$y = x + 8$

Step 2

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

$m_{1} = 1$

Step 3

Rewrite in slope-intercept form.

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Step 3.1

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

$y = m x + b$

Step 3.2

Subtract $x$ from both sides of the equation.

$- y = 2 - x$

Step 3.3

Divide each term in $- y = 2 - x$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- y = 2 - x$ by $- 1$ .

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

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.

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

Step 3.3.2.2

Divide $y$ by $1$ .

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

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 $2$ by $- 1$ .

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

Step 3.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 3.3.3.1.3

Divide $x$ by $1$ .

$y = - 2 + x$

Step 3.4

Reorder $- 2$ and $x$ .

$y = x - 2$

Step 4

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

$m_{2} = 1$

Step 5

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

$m_{1} = 1$

$m_{2} = 1$

Step 6