All '=' mean 'congruent to'

P1: 3x=5(mod2) --> x=1(mod2)

P2: 5x=4(mod3) --> x=2(mod3)

P3: 2x=1(mod5) --> x=3(mod5)

P4: 5x=6(mod7) --> x=4(mod7)

M1 is 210/2 = 105

M2 is 210/3 = 70

M3 is 210/5 = 42

M4 is 210/7 = 30

Therefore,

105*Y1=1(mod2) --> Y1=1(mod2)

70*Y2=2(mod3) --> Y2=2(mod3)

42*Y3=3(mod5) --> Y3=4(mod5)

30*Y4=4(mod7) --> Y4=2(mod7)

x equals 1*105*1 + 2*70*2 + 3*42*4 + 4*30*2 --> 1129

x=1129(mod210)

x=79(mod210)

Check:

Works for P1 and P2, but fails for P3 and P4.

Where'd I go wrong?!