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

SOLUTION

GIVEN:  

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)

TO DETERMINE

The value of q

EVALUATION

Here the given equation of the lines are

Now the two lines meet at the point (3,1)

Since equation (1) passes through the point (3,1)

Again Equation (2) passes through the point (3,1)

FINAL ANSWER

Hence the required value of q = 2