Solving a Linear System in Three Variables with no or Infinite Solutions - Problem 3

There are special cases for any system of equations where you have either no solution (meaning, the lines do not intersect at only one point,) or infinite solutions, meaning the lines intersect in some kind of line where there are infinite sets of numbers that would be solutions. (Note- with infinite solutions, not any random point will be a solution, but only the infinite set of points that lies on the solution line.) Algebraically, if your variables cancel out and you are left with a true equality statement like 0 = 0, then there are infinite solutions. If your variables cancel out and you are left with a false equality statement, like 0 = 2, then there is no solution to that particular system (often because there are parallel lines.)