Question

If the system of equations: 4x+py=21 and px-2y=15 has unique solutions , then which of the following could be the value of p?


103

105

192

197​

Answer 1

Consider the given equation.

4x+py=21

px−2y=15

The general equation,

$\bold{a_1x+b_1y=c_1}$

$\bold{a_2x+b_2y=c_2}$

So,

$\bold{a_1 =4,b_1=p,c_1 =21}$

$\bold{a_2=p,b_2 =−2,c_2 =15}$

We know the condition of unique solution

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

Therefore,

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

$\bold{ {p}^{2} \ne - 8}$

$\bold {p \ne2 \sqrt{ - 2} }$

$\small \bold{So, p is \: any \: real \: value \: except 2 \sqrt{2} }$