Finite Math Examples

$2 x + y = 510$ , $2 x + y = 810$

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 $2 x$ from both sides of the equation.

$y = 510 - 2 x$

Step 1.3

Reorder $510$ and $- 2 x$ .

$y = - 2 x + 510$

Step 2

Using the slope-intercept form, the slope is $- 2$ .

$m_{1} = - 2$

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 $2 x$ from both sides of the equation.

$y = 810 - 2 x$

Step 3.3

Reorder $810$ and $- 2 x$ .

$y = - 2 x + 810$

Step 4

Using the slope-intercept form, the slope is $- 2$ .

$m_{2} = - 2$

Step 5

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

$m_{1} = - 2$

$m_{2} = - 2$

Step 6