Question

$2x+3y+5=0$ and $px+6y+8=0$
The pair of equations given above have a unique solution for all values of $p$ except _______.

• A. $1$
• B. $2$
• C. $4$
• D. $8$

Answer 1

Answer: (C)

$4$

The pair of equations has a unique solution if:

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

For the given pair of equations: $2x+3y+5=0$ and $px+6y+8=0$;

$a_1=2;a_2=p;b_1=3;b_2=6$

For $\frac{2}{p}\ne \frac{3}{6}⟶p\ne 4$

Hence, the given pair of equations has a unique solution for all values of $p$ except $4$.