Question

Find the value of $p$ for which the given simultaneous equations have unique solution:

$8x-py+7=0;4x-2y+3=0$

• A. All values of $p$ except $4$
• B. $p=7$
• C. $p=6$
• D. All values of $p$ except $5$

Answer 1

The correct option is A All values of $p$ except $4$

As we know the condition for the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ to have a unique solution is -

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

Here the given system linear of equations is

$8x-py+7=0;4x-2y+3=0$

So for the unique solution

$\frac{8}{4}\ne \frac{-p}{-2}$

$\Rightarrow p\ne 4$