Hello,

The two given lines are

5x - 6y = 1 ...(i) and

3x + 2y + 5 = 0, i.e.,  3x + 2y = - 5 ...(ii)

Now, (i) × 3 and (ii) × 5, we get,

15x - 18y = 3 and

15x + 10y = - 25

On subtracting ( i ) and ( ii ), we get

- 18y - 10y = 3 + 25

So, - 28y = 28

Hence,  y = - 1

Now, putting y = - 1 in (i), we get

5x - 6 (- 1) = 1

So, 5x + 6 = 1

So, 5x = 1 - 6

Hence,  x = - 1

So, the point of intersection of the lines (i) and (ii) is (- 1, - 1)

Best Wishes.