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

Putting the value of x in eq. (i), we get

Hence, the point of intersection P(x₁, y₁) is

Now, we know that, when two lines are perpendicular, then the product of their slope is equal to -1

m₁ × m₂ = -1

⇒ Slope of the given line × Slope of the perpendicular line = -1

Slope of the perpendicular line

⇒The slope of the perpendicular line

So, the slope of a line which is perpendicular to the given line is

Then the equation of the line passing through the point having slope

y – y₁ = m (x – x₁)

⇒ 63x + 105y – 781 = 0