Solve the system WRITE ALL STEPS AND WRITE NEATLYSolutionx5

Solve the system. WRITE ALL STEPS AND WRITE NEATLY!

x=5 mod 7

x=7m+5

Case 1: m=0 mod 4

m=4n

x=28n+5 =1 mod 4

Case 2: m=1 mod 4

m=4n+1

x=7(4n+1)+5=28n+12=0 mod 4

Case 3: m=2 mod 4

m=4n+2

x=7(4n+2)+5=28n+19=3 mod 4

Hence, m=4n+2

SO,

x=28n+19, n=0,1,2,.....

x=28n+19=n+19 mod 27

So we can see that for n=8 mod 27 we have the solution

So, n=8 mod 27

n=27k+8

x=28(27k+8)+19=756k+243