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?