Question

Question 4 (iv)
Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Answer 1

Pair of equations is
$2x+3y-5=0$ ...(i)
$px-6y-8=0$ ...(ii)
Pair of equations have unique solution if
$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
Here, $a_1=2,b_1=3$ and
$a_2=p,b_2=-6$
$\Rightarrow \frac{2}{p}\ne \frac{3}{-6}$
$\Rightarrow 3p\ne -2\times 6$
$\Rightarrow p\ne -\frac{12}{3}$
$\Rightarrow p\ne -4$
Hence, the system of linear equations has unique solution for all real values of p except -4.