20. Two straight lines have equations $y=p x+4$ and $p y=q x-7$, where $p$ and $q$ are constants. The two lines meet at the point $(3,1)$.
What is the value of $q$ ?
A 1
B 2
C 3
D 4
E 5
20. B Since the point $(3,1)$ lies on both lines, we have $1=3 p+4 \ldots[1]$ and $p=3 q-7 \ldots[2]$. From [1], $3 p=-3$, so $p=-1$. Substituting for $p$ in [2] gives $-1=3 q-7$. Hence $3 q=6$. So $q=2$.