Consider the system of linear equations

Question

a₁x + b₁y = c₁

a₂x + b₂y = c₂

where a₁, b₁, c₁, a₂, b₂, and c₂ represent real numbers. What must be true about the lines represented by the equations when the following is true?

A: The lines must coincide.

B: The lines must be either parallel or coinciding.    

C: The lines must be parallel.

D: The lines must be perpendicular.

E: The lines must intersect at a point, but are not necessarily perpendicular.

Answer 1

If the slopes are the same the lines are parallel...

if the slopes and intercepts are the same the lines are the SAME...

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If the slopes are different, the lines will meet...

if the slopes are NEGATIVE RECIPROCALS of each other, they are perpendicular.

You did not provide any additional statement that is allegedly "TRUE", nor any

info. about the coefficients, so nothing else can be said.

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