Question

The pair of linear equations px + 2y - 5 = 0 and 3x + y - 1 = 0 has unique solution if

• A. $p=6$
• B. For all values of p except $p=6$
• C. $p=0$
• D. p has any value

Answer 1

The correct option is B For all values of p except $p=6$

$px+2y-5=0$

$3x+y-1=0$

Here $a_1=p,b_1=2,c_1=-5$ and $a_2=3,b_2=1,c_2=-1$

The given pair of linear equation has unique solution if

$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

$\Rightarrow \frac{p}{3}\ne \frac{2}{1}$

$\Rightarrow p\ne 6$

Hence the given pair of linear equation has unique solution for all real value of p except 6.