Question

The value of P for which the pair of equations 2Px + 3y = 7, 2x + y = 6 has exactly one solution. 

A) 3 

B) Any real number except 3 

C) Any real number 

D) For no real P the system has solution

Answer 1

Correct option is (B) Any real number except 3

For both lines has exactly one solution (unique solution), we have

\(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)

\(\Rightarrow\) \(\frac{2P}2\neq\frac31\)

\(\Rightarrow\) \(P\neq3\)

Hence, for any real value of P except 3, the given pair of linear equations has exactly one solution.

Answer 2

Correct option is B) Any real number except 3