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(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).

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ANSWER

See below

EXPLANATION

Given the system of linear equation:

[tex]y = m_1x + b_1[/tex]

[tex]y = m_2x + b_2[/tex]

If

[tex] m_1 \ne \: m_2[/tex]

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

If

[tex]m_1 =m_2 \: and \: b_1 \ne \: b_2[/tex]

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

If

[tex]m_1 =m_2 \: and \: b_1 = \: b_2[/tex]

Then, the two equations will coincide.

There is infinitely many solutions.

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