Question

Question 4 (iii)
Find the value(s) of p for the following pair of equations – 3x + 5y = 7 and 2px – 3y = 1,
If the lines represented by these equations are intersecting at a unique point.

Answer 1

Pair of equations is
$-3x+5y=7$ ...(i)
$2px-3y=1$ ....(ii)
For unique solution, we have $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
Here, $a_1=-3,b_1=5$ and $a_2=2p,b_2=-3$
$\Rightarrow \frac{-3}{2p}\ne \frac{5}{-3}$
$\Rightarrow 10p\ne +9$
$\Rightarrow p\ne \frac{9}{10}$
Hence, the given equations have unique solution for all real values of p except $\frac{9}{10}$.