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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}y = -2x^2 + 2\\y = 2\left(x^4 - 2x^2 +1\right)\end{array}\right. $

$(0,2),(-1,0),(1,0)$

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Campbell University

Oregon State University

Harvey Mudd College

Idaho State University

Okay, so this question were asked to, uh, solar system of equations using institution. Thankfully, the way the problem has set up, we don't even up to manipulate anything to sell for. Why? Because literally get to us in a format where? Why do you think so? You can just go ahead and set. Uh, why? Why, uh, or the substitute form of why so two X plus two said it equal. Thio treks to the fore, minus for X square plus two from here. Will you see that our shoes will cancel out. And then if we move the two x squared over Tillie's other side and get two extra before you're minus two, X squared is equal to zero. Okay. And then if we solve for X, come here. I got back square. We're left with X squared minus one. It's equal to zero, which is save us to x square. X plus one X minus. One is equal to zero. Uh, so we get that X is equal to zero. X is equal to negative. One X is equal to one. Okay, so when X is equal to zero, you putting it in tow may be pertinent to this sign equation because I know that Y is equal to negative two X squared plus two. Hey, that y is equal to two. And then when X is negative one, you get that by its equal to zero when X is one we hit that Y is equal to zero as well, because they are the coordinates of the intersections between the two functions. The back. It just proves that these are correct. And so, uh, if you look at the graph, could see that thes tune functions do intersect that zero to negative 10