Question

If the system of equations $4x+py=21$ and $px-2y=15$ has unique solutions then which of following is true?

• A. $p\ne 2\sqrt{-2}$
• B. $p\ne 2\sqrt{2}$
• C. $p\ne 2$
• D. $p\ne \sqrt{-2}$

Answer 1

Answer: (A)

$p\ne 2\sqrt{-2}$

Consider the given equation.

$4x+py=21$

$px-2y=15$

The general equation,

$a_{1}x+b_{1}y=c_1$

$a_{2}x+b_{2}y=c_2$

So,

$a_1=4,b_1=p,c_1=21$

$a_2=p,b_2=-2,c_2=15$

We know the condition of unique solution

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

Therefore,

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

$p^2\ne -8$

$p\ne 2\sqrt{-2}$

So, $p$ is any real value except $2\sqrt{-2}$.

Hence, this is the answer.