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

x – y = 1 …(i)

2x – 3y + 1 = 0 …(ii)

Now, we find the point of intersection of eq. (i) and (ii) Multiply the eq. (i) by 2, we get

2x – 2y = 2

or 2x – 2y – 2 = 0 …(iii)

On subtracting eq. (iii) from (ii), we get 2x – 3y + 1 – 2x + 2y + 2 = 0

⇒ -y + 3 = 0

⇒ y = 3

Putting the value of y in eq. (i), we get x – 3 = 1

⇒ x = 1 +

⇒ x = 4

Hence, the point of intersection P(x1, y1) is (4, 3)