I'm an engineer at an industrial plant simultaneous equations are very common in engineering problems. Just about any "optimization" problem can be represented

I'm an engineer at an industrial plant simultaneous equations are very common in engineering problems. Just about any "optimization" problem can be represented as a system of simultaneous equations even very complex non-linear dependencies are modeled like this. i.e a common problem such as calculating the optimal blend of fuel in a reactor is done based on solving a system of linear equations with constraints such as Loss on ignition, maximum allowable ash content, minimum specific energy etc. Industrial design as well uses simultaneous equations extensively. Do you want to build your aircraft wing out of CFRP or a titanium alloy? One way is to use a constraint based selection method something like strength to weight ratio vs cost. edit: I should add 99% of the time these are solved programmatically with the aid of a computer. You do not solve these problems "high school math style".