Question

The points $(3,-1)$ and $(6,1)$ lies on the line represented by the equation $px+qy=9,$ find the values of $p$ and $q$.

• A. $p=-8,q=-3$
• B. $p=-6,q=-3$
• C. $p=2,q=-3$
• D. $p=8,q=-3$

Answer 1

Answer: (C)

$p=2,q=-3$

Since the points $(3,-1)$ and $(6,1)$ lies on the line with equation $px+qy=9$, therefore, the equations will be as follows:

$3p-q=9$ ......(1)

$6p+q=9$ ....(2)

Adding equations (1) and (2), we gate

$(3p+6p)+(-q+q)=9+9$

$\Rightarrow 9p=18$

$\Rightarrow p=2$

Now substitute the value of $p$ in equation (1), we get

$6-q=9$

$\Rightarrow -q=9-6$

$\Rightarrow -q=3$

$\Rightarrow q=-3$

Hence, $p=2,q=-3$.