I'm an undergraduate student taking multivariable calculus. When discussing Lagrangian Multipliers, we would end up with equations such as this: $$ \lambda2x=2x+y $$ $$ \lambda2y=2y+x $$ $$ 4=x^2+xy+y^2 $$ (This particular system is not of any particular importance. It's just an example from the textbook)
After staring at them for a few minutes, I realized I was never taught how to formally find solutions to more complicated systems of equations such as this one. Most of the resources I've found online are targeted towards high school math students, and don't really cover the more complicated process required to solve these. Are there any online resources that may be of help to me?
Alcumus is a problem database for contest math. It has a couple of topics that you can look up:
(It is still high school, but it's contest math, so the questions are trickier and usually more challenging than regular math).