A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel. A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions. These two situations occur when trying to solve for a system of equations.
There's a few vocabulary words to keep track of when you're doing system of equations. Of course because Math is like all about vocabulary, here's a couple of important words. First a system of equations is called Inconsistent if there is no solution because the lines are parallel. Remember parallel means there is no slope, and the solution would be, excuse me parallel doesn't mean no slope parallel means they have the exact same slope my fault. So if they have they have the exact same slope they'll be parallel and there'll be no solution, no solution because solution means where the lines cross and parallel lines never ever cross. That's one vocabulary word to keep in mind inconsistent means parallel no solution. A system of equation is called dependent when you have the same line written in two different forms so there are infinite solutions. Like for example let's just say I have the line I'm just going to graph it really roughly y=2x+3, I could call that exact same line using a different name if I multiply everything by 2 I'll have 2y=4x+6. That's the same equation written in different forms, so if my system of equations that I was given just had those two like that. That would give me a statement that would tell me I had dependent, I would get something when I solve that looks like 0=0 or 5=5 something that always true, because always true means infinite solutions. It doesn't matter what x or y values I plugged in there they would always work if I have the exact same line written in different forms. So those are two vocabulary words to keep in mind when you're working through systems of equations watch out if you get something like zero equals zero that means you're going to have the same line written in two different forms which we call dependent. If you get something like 5=6 something that's never true that means you have two lines that never cross because they're parallel.
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