"determine the point of intersection of the line 2x − y = 1 and the perpendicular from the point (3, 2) to the line"

2x - y = 1
y = 2x -1
slope = 2
perpendicular slope = -1/2

y = mx + c
y = -1/2 + c
at point (3,2)
2 = -1/2 (3) + c
c = 2 + 3/2 
c = 7/2
y = -1/2 x + 7/2
y + 1/2x = 7/2

2x - y = 1  (1)
y + 1/2x = 7/2  (2)

(1) + (2):
2x  + 1/2x = 1 + 7/2
5/2 x = 9/2
5x = 9
x = 9/5 sub into (1)
2x - y = 1 
2(9/5) - y = 1
18/5 - y = 1
y = 18/5 - 1 
y = 13/5

Ans: x = 9/5, y = 13/5