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Hi-/a Points]DETAILSZILLDIFFEQ9 4.9.009.Solve the given system of differentia equations by systematic elimination Dx DZy est (Di+1)x (D =1)y BeStI(xce)y(t))lINeed H...

Question

Hi-/a Points]DETAILSZILLDIFFEQ9 4.9.009.Solve the given system of differentia equations by systematic elimination Dx DZy est (Di+1)x (D =1)y BeStI(xce)y(t))lINeed Heip?RoudllIatchltMsubm Answan

Hi-/a Points] DETAILS ZILLDIFFEQ9 4.9.009. Solve the given system of differentia equations by systematic elimination Dx DZy est (Di+1)x (D =1)y BeSt I(xce)y(t))l INeed Heip? Roudll Iatchlt Msubm Answan



Answers

Solve each system by the elimination method or a combination of the elimination and substi- tution methods.
$$ \begin{array}{r} {-2 x^{2}+7 x y-3 y^{2}=4} \\ {2 x^{2}-3 x y+3 y^{2}=4} \end{array} $$

I'm going to solve this system using the elimination method. So I'm going to start by multiplying equation one by two. And that gives us 10 X squared minus four y squared equals negative 26. And let's leave Equation two alone. So we have three x squared plus four y squared equals 39. So notice what's going to happen when we add these equations because one of them has negative four y squared and the other one has positive four y squared those white terms, we're going to be eliminated, so that gives us 13 X squared equals 13. So dividing by 13 we get exploit equals one and then taking the square root, we get X equals plus or minus one. Okay, now that we know the X coordinates, we need to find the white coordinates. So what we can do is go back to one of our equations. It doesn't matter which I'm just going to use equation too, and substitute these X coordinate in. So let's start with X equals one. So we have three times one squared plus four y squared equals 39 so that would be three plus four y squared equals 39 and subtracting three from both sides. We get four y squared equals 36 divided by four, and we get y squared equals nine and then square root. And we get why equals plus or minus three. So we have to ordered pairs. We have 13 and we have one negative three. Now let's find the white coordinates for X equals negative one. So we'll do the same thing We have three times negative. One squared plus four y squared equals 39 negative. One squared is the same thing as one squared. So this is going to work out to be the same. Um, Why values? So we end up with same idea of the other side. Why equals plus or minus three? So we have the ordered pairs negative 13 and negative one negative three.

In the question we have to solve the government system. Using elimination the government system is two weeks minus three Y. is equal to -7. five x plus four y. His equal Stone 17. Now moving towards the solution, let it be the question 100 with the question too. Now multiply equation one x 4. So you will get four and 22 X minus three Y. As opposed to four into minus seven. That is eight x minus 12. Y will be equal to minus 28. Now multiply equation too by three you will get three and to five X plus four. Y is close to 17, that is 15 X plus 12. Y will be by to 51. Now we can eliminate by using equation three and 4. Let it with question 100 with the question three. Now subtract equation three from subtracting question four from equation three you will get a tax minus 12 Y equals minus 28 minus 15 X Plus 15 x plus 12 y equals to 15 months. This will cancel out each other so 23 X would be equal to 23. That is X would be equal to one. Now we can put develop forex in any of the equation. So putting developed for X two into one minus three. Y equals two minus seven. So why would be equal to three? And the solution to this question would be 1:03. Thank you.

For this problem, we want to solve the system of equations two x minus three Y equals negative seven and five X plus four Y equals 17. Using elimination. Now the first thing that we can do here is multiply our first equation there by five so that we can get a five X. The top. In fact, let's multiply by negative five. So we'll get negative 10 x Uh minus or rather plus now 15 wide equals uh then there would be positive seven times 5, Which is going to be 35. Yeah. Then we can multiply the second equation by two. So we'll get 10 x plus eight Y Equals 17 times two is going to be 34 I believe. Now what we can do is add the two equations together. The exes will be eliminated and we'll have 15 Y plus eight Y. 15 Y plus eight Y is going to give us 23 Y. And that is going to equal 35 plus 34 Is going to be 69. Then we can divide both sides by 23. Yeah. Which gives us three. So we now have the Y equals three, so we can substitute that back into our beginning equations. Let's substitute it back into one. So we'll have that two x minus three Y. So that's going to be minus nine is equal to negative seven. Therefore two X is equal to nine minus seven, so two X equals two, so X equals one.

Okay, here's our system, and we're going to solve it using the elimination method. So I'm going to multiply the second equation by three and leave the first equation alone. So starting out by just rewriting the first equation and then multiplying the second equation by three, we get negative three X squared, minus nine. X Y Class three y squared equals nine. And we do that so that if we add the two equations together, we eliminate the X squared terms and we eliminate the Y squared terms as well. And what we have left is negative. Seven. X y equals 14. Let's divide both sides by negative seven, and we have X Y equals negative, too. We also want to isolate X or Y in this. So let's isolate X. We have X equals negative to over why. So now let's go back to one of our original equations and see if we can solve for some new miracle answers. So let's substitute negative to over why in for X in the second equation. So they have the opposite of negative two over why squared minus three times Now here's another substitution I want to do. Remember we found that X Y is negative two. So I'm going to substitute negative to and for X y. So we have negative three times negative, too. Plus y squared equals three. Okay, let's simplify this. So we have the opposite of four over y squared plus six plus y squared equals three. Let's multiply both sides of that equation by Y squared to clear the fraction. We can only do that if we know that Why is not zero? And we do know that why is not zero? Because we know that extends. Why is negative two okay, So multiplying both sides of the equation by y squared gives us negative four plus six y squared plus y to the fourth Power equals three y squared. Now I want to get all the terms over to the left side of the equation and treat this like a quadratic and factor it. So we have y to the fourth plus three y squared minus four equals zero. Let's see if we can factor that. That would be why squared plus four times y squared minus one set each factor equal to zero and we end up with y squared equals negative four. So this one gives us imaginary or non real solutions. We get y equals plus or minus two I and then we have y squared minus one equals zero. So y squared equals one. And why equals plus or minus one? Okay, we have four different y values and we need to find the corresponding X values. So let's go back to X equals negative to over way. So let's start with why equals to I. So then X is going to be negative to over two i, which is negative one over I but we don't leave an eye on the bottom. So let's multiply the top in the bottom by negative I So that will make it I over one. So X is I OK? So that point is I comma two. I now suppose why is negative two I so x is negative two over negative to I which would be one over I again. Let's not leave an eye on the bottom so multiplied by negative I over negative I get negative by over one negative I So that point is negative. I comma negative to I Now suppose that why is one again X is negative. Two over. Why so negative to over one is just the nice number. Hoops. Let me let me make that look better X is negative to over one. So that's just negative too. So we have the point negative to one. And finally, if why is negative? One X is negative two over negative one, which is to So we have the point to negative one. So we have four solutions I to I negative by a negative to I negative 21 and two negative one.


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