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What is the missing number so that this equation has 0 solution

-5x+20=__x-2

User Flaugh
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1 Answer

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we can look at the equation above as some system of equations with two variables, and one equation is say y = -5x + 20 and another is y = Kx-2.

Now, the question will boil down to, what makes that system of equations have no solutions?

Well, usually in a system of equations we can see the no solution part, usually means both lines are parallel or they simply just don't intersect, we can see it with a simplification that makes no sense, like 25 = 17, or 0 = 5.

Now, how can we make that system above make no sense? hmmm how about if just make the "x" cancel out?


\begin{cases} y=-5x+20\\ y=Kx-2 \end{cases}\hspace{5em}-5x+20~~ = ~~Kx-2 \\\\\\ -5x+20~~ = ~~\boxed{-5x}-2\implies \stackrel{ \textit{what the heck!?} }{20~~ \\e ~~-2}\qquad \stackrel{\textit{another way to say}}{\textit{\underline{no solution}}}

User David Braun
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