Solving a System of Linear Equations in Two Variables - Problem 10

Recall that in solving a system of equations, you are trying to find the point where your lines cross. If you have two lines, there are three scenarios: the lines cross in exactly one point (which is called independent and consistent,) the lines are parallel and never cross (which is called independent and inconsistent and you'll have no solution,) and the two lines are the same line written in different forms (which is called dependent and consistent and you will have infinite solutions.) If you are solving algebraically, both variables cancel out and you are left with a true statement like 0 = 0, then the solution is dependent and has infinite solutions. If both variables cancel out and you are left with a false statement like 0 = 2, then you have no solutions and an inconsistent system.