Question

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

$3x+y=10;9x+py=23$

• A. $p=5$
• B. All values of $p$ except $7$
• C. All values of $p$ except $3$
• D. Cannot be determined

Answer 1

The correct option is C All values of $p$ except $3$

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 of linear equation is

$3x+y=10;9x+py=23$

So for unique solution, we have

$\frac{3}{9}\ne \frac{1}{p}\Rightarrow p\ne 3$