Question

(HELP PLEASE)

Describe in your own words the characteristics of linear equations that determine whether a system of linear equations will be Intersecting, Parallel, or Coincident. (2 points, 0.5 for clarity of response, 0.5 for each type of system).

Answer 1

See below

Step-by-step explanation

Given the system of linear equation:

`y = m_1x + b_1`

`y = m_2x + b_2`

If

`m_1 \\e \: m_2`

then the two equations, will intersect at one. The system has unique solution.

If

`m_1 =m_2 \: and \: b_1 \\e \: b_2`

then, the two equations are parallel and the system will not have a solution.

If

`m_1 =m_2 \: and \: b_1 = \: b_2`

Then, the two equations will coincide.

There is infinitely many solutions.