I'm going through the Brillient.org Algebra 1 course, and I came across a problem that I don't think was well explained, and I'm hoping I can find more insight here.
So this type of problem, for some background, has a numeric value on each of the rows and columns, by which you can assemble equations to find the values of each of the items in the squairs.
an example would be each row has a few different shapes... squair, circle, triangle... etc and the far right side would have a summed numerical value for those shapes, as well as the bottom... your goal is to find the values of each of them using linear programming. So you end up with 6 total sums. But according to the answer of this problem.. you can only ever have 5 unknowns even though there are 6 equations. I know it has something to do with linear dependence, but I'm not sure how you can prove that in an intuitive way.
The solution is there can be 5 unknowns max, but I don't understand why. I would be truly grateful if someone could explain this and how they got to that fact? And is this generalizable to larger puzzles? I understand the idea of linear dependence/independence, I just don't fully understand how you can prove this fact in this abstract form.
