Remember to pay close attention when adding all the like terms and remember to show all your work because it is very easy to make mistakes, especially when you have four variables.
Step 1: You first find a common denominator and multiply it to the four varaibles. Once you've done that you add up all the like terms and separate them into the common terms. Then, you can start canceling out the like terms and the results will be the system.
Step 2: Next, you take the first and second equations and add them together. Then, you can use the elimination method in the third and fourth equation, in the picture above, I eliminated D. Once you have the two equations, you use elimination on them as well and I eliminated C.
Step 3: This picture shows what I did to solve for the four variables. The picture is pretty much self-explanatory. I just solved for A first and then used the substitution method to find the other equations.
This will be your final answer in the end.