Question

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

Answer 1

Point (3, $-$1) lies on the line px + qy = 9.

$$\begin{gathered} \therefore p\times 3+q\times \left(-1\right)=9 \\ \Rightarrow 3p-q=9...\left(1\right) \end{gathered}$$

Again, point (6, 1) lies on the line px + qy = 9.

$$\begin{gathered} \therefore p\times 6+q\times 1=9 \\ \Rightarrow 6p+q=9...\left(2\right) \end{gathered}$$
Adding equations (1) and (2), we get:
$$\begin{gathered} 3p-q=9 \\ \underline{6p+q=9} \\ 9p=18 \\ \Rightarrow p=\frac{18}{9}=2 \end{gathered}$$
Substituting the value of p in equation (1), we get:

$$\begin{gathered} 3p-q=9 \\ \Rightarrow 3\times 2-q=9 \\ \Rightarrow 6-q=9 \\ \Rightarrow 6-9=q \\ \Rightarrow q=-3 \\ \therefore p=2\mathrm{and}q=-3 \end{gathered}$$