I used to come across linear algebra problems in math class that seemed impossible to solve. Consider trying to find the value of x, y, and z given this set of two equations:

4x + 3y + z = 8

x + y = 2

If I plug this into Wolfram Alpha, all it can tell me is "y = 4 - x". That doesn't solve for x, y, and z like we want. The problem is intractable.