Question

Two straight lines have equations y = px + 4 and py = qx - 7 where p and q are constants. The two lines meet at the point (3,1). What is the value of q?

Answer 1

Given:

Equations of two lines are

$y=px+4$

$py=qx-7$

where, p and q are constants.

The two lines meet at the point (3,1).

To find:

The value of q.

Solution:

We have,

$y=px+4$           ...(i)

$py=qx-7$          ...(ii)

The two lines meet at the point (3,1). It means both equations must be satisfied by the point (3,1).

Putting x=3 and y=1 in (i), we get

$1=p(3)+4$

$1-4=3p$

$\dfrac{-3}{3}=p$

$-1=p$

The value of p is -1.

Now, putting p=-1, x=3 and y=1 in (ii), we get

$(-1)(1)=q(3)-7$

$-1+7=3q$

$\dfrac{6}{3}=q$

$2=q$

Therefore, the value of q is 2.