.
Unfortunately, the post is written and submitted by a person, who does not understand the meaning of the words he uses.
Explanation
(1) If TWO separate equations are presented in the post, then wording must be THIS :
Solve equations 3x = 1(mod 7) and 5x = 1(mod 8)
using plural "equations".
(2) If one entity is assumed, then wording must be THIS :
Solve the system of two equations 3x = 1(mod 7) and 5x = 1(mod 8)
using the term "system".
I will assume the formulation #2.
Solution
First equation, 3x = 1(mod 7), is equivalent to x = 5(mod 7).
Second equation, 5x = 1(mod 8), is equivalent to x = 5(mod 8).
Then the system is equivalent to one equation x = 5(mod 56).
ANSWER. The solution to the system is x = 5(mod 56).
