I am a maths teacher and I'm looking for practical examples of measuring quantities simultaneously, so that mathematically one needs to construct and solve a system of equations. I thought that in the world of chemistry there could well be many possible such problems, but alas I have no experience of chemistry, hence I thought to ask here.
I searched online and found two possible situations.
Given an alloy of say two metals, we can use the combined weight as one equation and the combined volume as a second equation and hence we can find the amount of each metal in the mixture. What I like about this is the simplicity whereas I assume it is much more difficult to extract the metals separately.
Given a mixture of two gases, we can see how much light of one frequency is absorbed and again for a second frequency which allows the amount of both gases to be simultaneously found.
What other such situations are there is chemistry; when would one actually need to do such simultaneous calculations?