The line (p+2q)x+(p−3q)y=p−q.for different values of p and q passes through the fixed point

We have,(p+2q)x+(p−3q)y−p+q=0⇒ p(x+y−1)+q(2x−3y+1)=0Clearly, it represents a family of lines passing through theintersection of the lines x+y−1=0 and 2x−3y+1=0.The coordinates of the point of intersection these two lines are(2/5, 3/5).