Ellis\textquotesingle s Eel Emporium contains a large tank holding three different types of eel: electric eels, moray eels and freshwater eels. A notice on the tank reads as follows:  All the eels are electric eels except for $$12$$  All the eels are moray eels except for $$14$$  All the eels are freshwater eels except for $$16$$  How many eels are in the tank? 
Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems
Let the number of electric eels be $$x$$, the number of moray eels be $$y $$ and the number of freshwater eels be $$z$$. The information on the notice tells us that $$y + z = 12$$, $$x + z = 14$$ and $$x + y = 16$$. When you add these three equations, you obtain $$2x + 2y + 2z = 42$$ and hence $$x + y + z = 21$$. Therefore the number of eels in the tank is $$21$$. 