Hello all,
I am currently taking a History of Mathematics course at university level.

Unfortunately I am now stuck on one of the questions:

Find a positive integer solution to the equation 350x +1 = 99y
Use the technique of Bashkara. Give your answer as the possible smallest integer


I have access to the previous year's solution when the equation was 250x +1 = 87y


Euclidean algorithm
250 = 2*87 + 76
87 = 1*76 + 11
76 = 6*11 + 10
11 = 1*10 + 1

Step 2:
2 2 2 2 23
1 1 1 8 8
6 6 7 7
1 1 1
1 1
0

Possible solution: x = 8, y = 23



I understand step one of the question, and have worked out the following for this year's equation (350x +1 = 99y)
350 = 99*3 + 53
99 = 53*1 + 46
53 = 46*1 + 7
46 = 7*6 + 4
7 = 4*1 + 3
4 = 3*1 + 1
3 = 1*3 + 0


But can someone explain to me what is going on in step 2, I am totally lost here.

Thank you very much!