Find the equation of the line through the intersection of the lines 5x – 3y = 1 and 2x + 3y = 23 and which is perpendicular to the line 5x – 3y = 1.
Find the equation of the line through the intersection of the lines 5x – 3y = 1 and 2x + 3y = 23 and which is perpendicular to the line 5x – 3y = 1.

Answer : Suppose the given two lines intersect at a point P(x1, y1). Then, (x1, y1) satisfies each of the given equations.

5x – 3y = 1 …(i) 2x + 3y = 23 …(ii)

Now, we find the point of intersection of eq. (i) and (ii) Adding eq. (i) and (ii) we get

5x – 3y + 2x + 3y = 1 + 23

⇒ 7x = 24