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# In Exercises 11 - 20, solve the system by the method of substitution. Check your solution(s) graphically. $\left\{\begin{array}{l} \hspace{1cm} x + y = 0\\x^3 - 5x - y = 0\end{array}\right.$

## $(0,0),(2,-2),(-2,2)$

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### Video Transcript

for history. Given two equations in the system we have X plus y is equal to zero. We also have X cubed minus five X plus y eyes go to zero and were asked to solve this using substitution. I'm going to use this upper equation to sew for why and why is equal to negative X and then use this to plug into this bottom equation, which will get X cubed minus five. X minus. X is equal to zero, which is the same as X cubed, minus minus two. Okay, You know, I miss robbed, Mister, Is this should be Should be a minus y. I just, uh this right this way. Okay, so excuse minus five x plus, uh, plus X plus X. People 2 to 0, which is the same as X cubed minus for X is equal to zero on, then this. If we factor out an extra get X squared minus four is equal to zero, which is equal to X times X minus two X plus two is the host to Nero, and then we get that X is equal to zero. X is equal to two. X is equal to negative, too if we put this into here to Sophie, why we get coordinate points at 00 too negative two and negative to cause it to on dso photograph it. The graph does intersect at those three points. So we know that weeks off sould be a substitution correctly. Both grafts here to see that it does intersect on negative 2200 and united.

University of Texas at Austin

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