Given:
Equations of two lines are
[tex]y=px+4[/tex]
[tex]py=qx-7[/tex]
where, p and q are constants.
The two lines meet at the point (3,1).
To find:
The value of q.
Solution:
We have,
[tex]y=px+4[/tex] ...(i)
[tex]py=qx-7[/tex] ...(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
[tex]1=p(3)+4[/tex]
[tex]1-4=3p[/tex]
[tex]\dfrac{-3}{3}=p[/tex]
[tex]-1=p[/tex]
The value of p is -1.
Now, putting p=-1, x=3 and y=1 in (ii), we get
[tex](-1)(1)=q(3)-7[/tex]
[tex]-1+7=3q[/tex]
[tex]\dfrac{6}{3}=q[/tex]
[tex]2=q[/tex]
Therefore, the value of q is 2.
