5

Sotn: X -3y+2-$ 2x-Y" -2 4*-3z-0 0 6= Y.2-(4 2.0) (x Y 2- 25 (3.19. 4 OcNo solulion Od (xY.2)-(-25_ 25 25) 19 OL Infinite solutions 06 (x.%.2)- (3.19.4)OLYL In...

Question

Sotn: X -3y+2-$ 2x-Y" -2 4*-3z-0 0 6= Y.2-(4 2.0) (x Y 2- 25 (3.19. 4 OcNo solulion Od (xY.2)-(-25_ 25 25) 19 OL Infinite solutions 06 (x.%.2)- (3.19.4)OLYL Intrd& sts eauna Homen bolti Dearrsic male Quab Iban tha #nan Inai tha sratorn havo ninia MenY 8041o1i?

Sotn: X -3y+2-$ 2x-Y" -2 4*-3z-0 0 6= Y.2-(4 2.0) (x Y 2- 25 (3.19. 4 OcNo solulion Od (xY.2)-(-25_ 25 25) 19 OL Infinite solutions 06 (x.%.2)- (3.19.4) OLYL Intrd& sts eauna Homen bolti Dearrsic male Quab Iban tha #nan Inai tha sratorn havo ninia MenY 8041o1i?



Answers

Solve each system. Use any method you wish. $$ \left\{\begin{array}{r} 2 y^{2}-3 x y+6 y+2 x+4=0 \\ 2 x-3 y+4=0 \end{array}\right. $$

Hello. You are todavia going to soar from the number 20 things he had. The given function is six x squared by double s plus seven X ray minus two. Right, because zero here. A Joseph B seven. See cause minus two six square plus and minus six, sir. Minus two equals zero. So six square plus R minus two kick or zero baker are recorded one by two comma minus two by three. So why off? There isn't Gordo. It's even. It was a bubba one By doing so there. See to it that the par minus two by 3% sub student there equals and X wealth X is a core Do see even if you did a bar one by doing Len, if plus see to it is a power minus two by three into l n f. But is it Goto? See you are exit a bar run by. Do see though X to the power minus two by three. Okay, here initial conditions argument. So you take in order to find Siyuan Dancinto? So you need a friend? Agents are like really right off my is a card. 00 So by off exit car tow Seaver Extra apartment by toe. Plus seem to excell apart off my nostril by three equals zero C one plus c toe pickle. Syria is a fast one. Okay. Similarly, why would I? Self mark equals smart when I saw thanks you think will do. See you are I'm They go. Example minus and big. See you till minus two by three extra part off minus 5.3 if you substitute. Be good si won by two minus tools into by three. You go to smart. You know we see when we goto minus c therefore negative minus settle, Baikal. My nostrils. April by three equals life. If we saw Regan, Cebu equals minus six by seven. See, You're Nichols six place. My affects will be called. Oh, my ex is in cargo six by seven extra. The bar. When they do, then my last six by seven. Acceptable minus two by three. Thank

So what we're being asked to find in this problem is if this table X and Y values correspond to a function and so basically the concept is if an ex value that is given as more than one, why value the table cannot be a function. So we see here that this X value of 25 are here as a Y value of five. And then if we keep looking at this table we see at the bottom that X being 25 also has a value of negative five. So if we put this on a graph X and like word nus, we see that when X is 25 why can be either five were negative five, meaning that this cannot be a function. And also the X value of one corresponds multiple. Why values along with the X value of nine? So this table of access my values, is not a function

For this problem were asked to solve the system of equations. So because my ex square wide square lined up, I'm gonna solve this by using the elimination method. So the first thing I'm gonna do is make both on the number of x square to be six. So that I can eliminate the X squared. So for the first equation I need to multiply by um three. So therefore my equation here is going to become uh actually I'm going to multiply by negative three. So that negative six plus six is gonna give you zero. So therefore we have negative six negative six over X square Plus nine over wide squared -3 equals to zero. And then for the second equation you're just gonna bring down. So that's six over X squared minus seven over wide squared plus two equals to zero. So now I can add these two equations together. So the negative six plus six. So the X corps is gone and the negative nine plus plus negative seven. So basically nine minus seven, I can add these two fractions because they have the same denominator here. So therefore that's going to give us to over Wide squared equals two, negative three plus two. Gonna give us a negative one. So that's gonna be minus one equals to zero. So now I can sell for Wide by adding one. So this will be to over wide Square equals to one and multiply both sides by wide square to get rid of the fraction. So we have two equals two Y squared. And uh to solve for why we're going to take the square root, so why it's going to be equal to positive or negative square too? So now we know why equals two. Now we're gonna plug that answer into one of the the equations here. So I'm gonna plug into the original equation. The two over X squared minus three over wide score plus one equals to zero. So therefore we have here two over X squared -3 over wide square. Why I'm going to start with positive score two squared plus one equals to zero. So now I'm going to solve this equation. So we have two over X squared -3 over the square to square the square and square cancels out. So that's just going to give you two plus one equals to zero and the negative three plus negative 3/2 plus one. That's going to give you, so we have two X squared. So this one you can change it to two over to have the same denominator. So that's going to give you negative one half equals to zero. So now we have two over X squared equals to one half. And now I'm gonna cross multiplies. So we have four equals two X squared and square root to software X. So X is is either going to be positive or negative too. So therefore when my wife value is Square two I have two different x values. one is positive too and the other one is going to be negative too. So now let's plug in the negative school to for the Y. So when we plug in the negative for the for the white, the negative square to square is still going to be too because any negative numbers square is going to be positive. So therefore we get the same X values when we plug in the negative square to so therefore When your wife value is negative school to negative school to your excess values are two and -2. And these are the solutions for this system of equation. And you can verify that by plugging each one of these points into your system of equations.

Well this question we're asked to solve this system of equations using any method. So because X squared and wide square lined up, we can solve this system of equations using the elimination method. So I'm going to um move the constant to the other side. So we have x squared minus three. Y squared equals two naked one. The second equation is two, X squared minus seven. Y squared equals two negative five. And you can either eliminate the X square or eliminate the wide square. Okay, so in this problem seems a lot easier if you eliminate the X square where you only have to multiply one equation. So for the first equation I'm going to multiply by negative two. So therefore we have negative two, X squared plus six, Y squared equals to two. So now I can add them together because two plus negative to become zero. So your ex square is gone. So therefore you have negative y squared equals two negative three. And when you divide by negative one on both sides, y squared equals two positive three. And when you take the square root, why can be either equal to positive square three or it can be equal to negative score three. So to find the white value, you're gonna plug into one of these equations. So I'm going to plug into our first equation. So we have X squared minus three times. Why? Why? Here is gonna be let's start with positive score three squared plus one equals to zero. So we have here X squared the score or three square gives you 33 times negative three. It's gonna give you negative nine plus one equals to zero. So X square is minus eight equals zero. So now I'm going to add eight so X equals two positive eight. And when I take the square root eight, eight I can rewrite this as the school of four times square root of two. So therefore X. Can be equals to plus or minus two, squirrel too. So therefore when why is positive score three X. Value can be positive to square two or the X value can be negative two square or two. And now let's plug in the negative score of three into our equation here. So when I plug in negative score of three square, you will notice that I still get nine because negative score three square is going to give you positive three again and three times negative three is negative nine. So you still get the same X. Value. So therefore we have two more solutions. When why value is negative screw three. We have the same X. Values to screw to and when why various negative score three. Your X value can be negative to score or two. And you can verify your solution by checking by subsidy these X and Y into your system of equations. But all those four do work when you when you check them on your own.


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