Dear Algi, Absolute Values seem pretty easy on the surface. I mean, all you have to do is make everything positive, right? And systems? Child’s play! Or so I thought. Until my Algebra teacher had to burst my bubble and declare that if we REALLY want to prove we know Algebra, we should be able to find the intersection points of the equations:

y = 3|x - 3| + 3
y = -⅔|x - 5| + 6

3|x - 3| + 3 = -⅔|x - 5| + 6

both graphically AND through algebraic work.

So I started this problem, full of promise. I can do this! I thought. Then suddenly, out of nowhere, I was thrown into a dark spiral. My algebraic work predicted 4 solutions My Algebra teacher says that I should be able to explain this, but I am lost. Are all these solutions there? And if they aren’t real, why do they show up and RUIN MY LIFE? Please help me before I convince myself that I am losing it over solutions that don’t exist!