In Exercises 25–35, solve each system by the method of your choic...

Question

In Exercises 25–35, solve each system by the method of your choice.  This  is a piecewise function, refer to textbook problem.

Accepted Answer

Hello today we're going to be solving a system of equations using any method of our choice. So the equation is given to us is y. Is equal to X squared plus four. X plus four. And the second equation is X plus y is equal to zero. So how do we go about solving the system of equations? Well if you notice we are given a Y value based off of the first equation why is equal to everything on the right hand side. So we can go ahead and take y and directly substituted into our second equation to solve for X. Doing so is going to give us X plus X squared plus four, X plus four equal to zero. Now in order to solve for X we're just gonna go ahead and simplify and combining like terms together four X and X can combine to give us five X. So what we are left with is X squared plus five, X plus four equal to zero. Now this is a fact herbal trin Amiel factoring this is going to produce the values X plus four times X plus one equal to zero. Now what we're gonna do is set both of these values equal to zero. Doing so is going to give us X plus four equal to zero and X plus one equal to zero. And solving for both of these values is going to give us X is equal to negative four and X is equal to negative one. So we end up with two values for X. That means we're gonna have two sets of solutions. So in order to figure out what are Y values are gonna be. We're gonna have to take these values of X and plug them into one of our original equations. Well, the easiest equation to work with is going to be our second equation. So if we take X is equal to negative four and plug it in directly to our second equation, what we are left with is negative four plus Y equal to zero. In order to sulfur. Why we just go ahead and add negative four to both sides and we get Y is equal to four. And if we plug in X is equal to negative one to our second equation, what we get is negative one plus Y equal to zero in order to sulfur. Why? We just add one to both sides of this equation and why is equal to one. So in order to combine our solutions together, We know that X is going to equal -4 when Y is equal to four and X is equal to negative one when y is equal to one, that is gonna be the solutions to this equation. That also means that the answer to this problem is going to be a So I hope this video helps you in understanding how to use the substitution method and I'll go ahead and see you all in the next video

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

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