be equal to
103x+2 1 1y=57
103(x+2y)+5y=57
Let z=x+2y ①.
103z+5y=57
3z+5(y+20z)=57
Let w=y+20z ②.
3z+5w=57
Obviously, z=9 and w=6 are a set of solutions, or z= 19 and w=0 are also a set of solutions.
(If you can't see it, continue to exchange yuan:
3(z+2w)-w=57
Let u=z+2w.
3u-w=57=3* 19
Obviously, U = 19 and W = 0 are a set of solutions.
)
Then according to ① ②, we get
x = z-2(w-20z)=-2w+4 1z = 357 mod 2 1 1
Calculated by modulus
x= 146 mod 2 1 1
Is the solution of congruence.