In the Real World
Systems of equations can be amazingly useful. How else would you figure out how many ounces of 70% dark chocolate and 20% milk chocolate you need to mix to get one pound (16 oz) of 40% chocolate? We forgot to mention: the meaning of life involves mixing chocolate. There. Now you know.
While problems with two unknowns may seem impossible to solve at first, we can use a system of equations to organize our information, then use one of our three methods to solve the system and find the answer. Oh, organization. You are a cure for all ills.
This idea becomes even more useful when we allow the systems of equations to have more unknowns and more equations. Then we can solve for 3 things at once. Or 4, or 5, or 6. Not 7, though. Certainly not 7. All right, let's throw 7 into the mix.