Hi May,

In general, you would use Gaussian elimination or a similar method - preferably computing by machine!

Here, however, not all variables appear in all equations, and you can proceed by repeatedly doing the easiest thing that comes to hand. You cannot immediately find any one value, but you can rewrite the first equation as A = -C and use that to eliminate A from the other three equations.

Now there are only two variables in the third equation. It's not quite as simple, but you can put that into the form C = pD + q for some rational numbers p,q. Use that to eliminate C from the second and fourth equations.

You now have two equations in B and D only. (You probably know how to solve a system like this.)

Good Hunting!
RD