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Some systems of inequalities do not have a solution.

Just like dividing by zero yields no viable solution, sometimes there will be a solution that is not viable within a system of linear inequalities. Watch the video below which explores why this happens.
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When dealing with systems of equations, sometimes you have to think a little bit about the answer that you have. For instance, if I have these two lines, ok? And the overlapping is right here, ok? Yes, this is the answer to the actual systems of equations but if the context, for instance, is talking about making t- shirts, ok? And I pick this point right here, which is at the x coordinate of three point five, can I actually make three point five shirts? Meaning, can I make half of a shirt? No, I cannot. So in this type of problem when you’re dealing with production or anything, you have to think of can you make fractions of things or are you just dealing with the whole numbers that are in the solution?

Another example would be, say I have these with an overlapping of right here. In this case, we’re dealing with money or maybe with like a savings account, ok? So yes, again this overlapping again is the answer to the systems equation, but in the context of the problem dealing with money, I can’t really talk about having anything out here, because like with a savings account, you never have negative money, this is x is negative down here, x and y are both negative. You can never have a negative amount, so again, context is key with some of these problems, especially word problems. So when you are solving your system equations, sometimes you have to do a little extra thinking before you come up with your final answer.