Solve the pair of simlutaneous congruences by letting x 15q

Solve the pair of simlutaneous congruences by letting x = 15q + 8 x equivalence 8(mod15); x equivalence 11(mod14)

Solution

x=15q+8

x=15q+8=11 mod 14

15q+8=11 mod 14

15q=3 mod 14

q=3 mod 14, we used 15=1 mod 14

So, q=14p+3

So,

x=15(14p+3)+8=210p+53, where p is any integer