Find the equation of the line joining the point (3, 5) to the point of intersection of the lines 4 x+y−1=0 and 7 x−3 y−35=0.
The point of intersection of the lines
4x+y−1=0 and 7x−3y−35=0 is
y=1−4x
7x−3(1−4x)−35=0
7x−3+12x−35=0
19x−38
x=2
⇒ y=1−4x=1−8=−7
∴ Let P(2, −7) and Q(3, 5)
The equation of line PQ is
y−y1=m(x−x1)
y−y1=y2−y1x2−x1(x−x1)
y−(−7)=5−(−7)3−2(x−2)
y+7=12(x−2)
y=12x=−31
12x−y−31=0