Thanks for showing me how to work out some of the previous post.

I would like to check my answer for this problem

Find all incongruent solutions modulo 35 of the following system

7x + 5y = 13 (mod 35)

11x + 13y = 4 (mod35)

91x + 65y = 169 (mod 35)

-605x - 65y = -20 (mod 35)

=

514 = 149 (mod 35)

Euclidean Algorithm

514 = 14*35 + 24

35 = 1*24 + 11

24 = 2*11 + 2

11 = 5*2 + 1

Extended Euclidean Algorithm

1 = (1 * 11) + (-5 * 2)

= (-5 * 24) + (11 * 11)

= (11 * 35) + (-16 * 24)

= (-16 * 514) + (235 * 35)

= (235 * 35) + (-16 * 514)

35-4 = 31

Solution

x = 31 (mod 35)

77x +44y = 143(mod 35)

-77x -91y = -28 (mod 35)

=

36y = 115 (mod 35)

Euclidean Algorithm

35 = 0*36 + 35

36 = 1*35 + 1

35 = 35*1 + 0

Extended Euclidean Algorithm

1 = (1 * 36) + (-1 * 35)

= (-1 * 35) + (1 * 36)

115*36 = 4140

4140 / 35 = 118.28

118 * 35 = 4130

4140-4130 = 10

Solution

Y = 10 (mod 35)

I think im correct but not sure