Choose the correct answer from the given four options:
If a pair of linear equations is consistent, then the lines will be
(A) parallel
(B) always coincident
(C) intersecting or coincident
(D) always intersecting
Given:
A pair of linear equations is consistent.
To do:
We have to find the correct option.
Solution:
If a pair of linear equations is consistent, then it has a unique solution or infinite solutions.
For unique solution, the lines will be intersecting each other.
The required condition is,
$\frac{a_1}{a_2}≠\frac{b_1}{b_2}$
For infinite solutions, the lines will be coincident.
The required condition is,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
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