Question

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

Answer 1

Hint: In this question it is given that if a pair of linear equations is consistent, then we have to find the behaviour of these pairs of lines. So to find the solution we need to observe what happens when two linear equations coincide.

Complete step-by-step answer:
First of all let us consider the two linear equations are $$a_{1}x+b_{1}y+c_{1}=0$$ and $$a_{2}x+b_{2}y+c_{2}=0$$.
The system of two linear equations is consistent in the following two cases.
Case 1
When the lines are coincident then there are infinitely many solutions and the system is consistent
i.e, $$\dfrac{a_{1}}{a_{2}} =\dfrac{b_{1}}{b_{2}} =\dfrac{c_{1}}{c_{2}}$$
Case 2
When the lines are intersecting then the system has unique solution and system is consistent
i.e, $$\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}$$
Thus the correct option is option C.

Note: To answer this type of question you should keep in mind that whenever two lines are consistent then the lines either coincident or intersect with each other.