There are many posts about the CRT that deal with this type of question:
using CRT:
x congruent to a mod b
x congruent to c mod d
what is the least value of x?


However, how does one approach the solution to this:
2x + y congruent to a mod b
x - 3y congruent to c mod d


is this a first step?
multiply second equation by 2.
2x + y congruent to a mod b
2x - 6y congruent to 2*c mod d


or multiplication of equation 1 by 3
6x + 3y congruent to 3*a mod b
x - 3y congruent to c mod d

What is the procedure to solve such?

thanks


More specific:
There exists a bunch of red & blue easter eggs.
Alice determined that the total (red + blue) was 4 mod 13
and that the difference (red - blue) was 7 mod 17
red + blue congruent to 4 mod 13
red - blue congruent to 7 mod 17

How to proceed?