The complexities of three equations or three unknowns are no harder then 1000 equations with 1000 unknowns. There is a mathematical reason for understanding how to do it, and having a good grasp of the method and being able to do it.
The method you did was solving a system of linear equations.
There are quicker and easier methods with matrices.
But of course, any computer made in the last 20 years can do it in a heart beat. I have a 38 year old calculator I got from my father that can solve a 9 system of equations.
If the math in your chemistry classes are hard for you, great, you must learn something new. If the math in your classes are not actually leading to you learn some new scientific principle and is not hard just tedious and time consuming, your professor is doing something wrong.