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11 3 3] Solve the system 2 3 5 I = L2 3 ]...

Question

11 3 3] Solve the system 2 3 5 I = L2 3 ]

11 3 3] Solve the system 2 3 5 I = L2 3 ]



Answers

Solve each system. $$\begin{aligned} &\frac{2}{x}+\frac{3}{2 y}=\frac{11}{4}\\ &\frac{5}{2 x}-\frac{2}{y}=\frac{3}{2} \end{aligned}$$

So in this question, were given a system of three equations off three variables and were asked to find the solution to this system. So the first thing that I'm going to do is I'm just going to label these equations question one equation, too. An equation. Three. To help organize what we're going to do when we manipulate these equations. So the first thing we should always try to do is try to eliminate a variable if we can. If that's easy. And if we see right here, we see in Equation one, we have a coefficient on. Why, off to an equation to We have a coefficient of negative, too. So if I added equations one into together, we will cancel out the white term and we'll get an equation with only two variables instead. So let's go ahead and do that. I have to get if we do equations one and two added together, I'm gonna label that equation for and then we'll get three X plus four X is seven X. We'll get the wise that cancel out and then negative five Z minus three z is minus eight minus eight C and then three minus 10 will give us negative seven. And now, since we've already eliminated the white term, we want to try to get another equation with only X and Z so that we can solve that system instead. So if we look at Equation three, we noticed that the whites term is also also has a coefficient of negative, too. So we can kind of repeat what we just did before and eliminate why in the same fashion, by adding equations one and three together because one has a coefficient off to right here. And this one has an equation off negative, too. So I'll just call that equation. Five. We get by adding equations one and three together, and so you get three X plus five X is eight X and then to Y minus two. Why will those cancel out and then negative five Z minus two Z is minus 70 in that equals three minus 11 which is negative. Eight. So now that we've done that, we can go ahead and solve this system off two equations and two variables to solve for X and Z individually, and then we'll sell for why, after we've done this, So I can multiply the equation for by ah factor of eight. And then what's price equation five by a factor of seven. And then this will give us a common coefficient of backs. So if I multiply equation four by eight, let's just do that's right here. I'll just call that question six. Then if I want to play equation for by eight, we get 56 x minus 64 Z equals negative 56 and will multiply equation five by seven to get that same 56 as the coefficient of the Ekstrom. So for equation seven Most Plying Equation five by seven To get 56 x minus 49 z hoops 49 c ecause negative 56. So now we can eliminate the ex term because they're coefficients are the same. So if I do Equation six minus equation seven. We'll get 56 x minus 56 ex, which is just zero. So that cancels out will get negative 64 Z minus a negative 49 z. And so I'll just write that out minus negative 49 z and then a negative 56 minus an egg to 56 will just be zero. So then we're going to get negative 15 z equal zero, so Z has to equal zero. So after we've solved for Ze, now we can plug this Izzy value back into any one of these and solve for the ex term. So I'm just gonna pick equation for it. Doesn't matter which one you pick. So I have seven x question. Ford gives you seven X minus eight times zero equals negative. Seven. So minus eight times your is just zero. So this cancels out and we get seven. X equals negative seven. So if we divide by seven on both sides, we get X equals negative one. So we've solved for a second variable, and now all that's left to do is to solve For why? So we can go back to any of our original three equations and we can pick any one of those and plug in these two values and then saw for why, So I'll just pick equation one. So we have three x so three times negative one plus two. Why minus five times E, which was zero equals three. So we see that once again, the Z is a zero, so these this term cancels out. So we have negative three right here. Plus two. I equals three. And if we add three to both sides, then we'll get to why equal six and then dividing by two on both sides, we get why equals why? Because three. And now we have all three variables. So we now have a solution to this system of three equations, which is going to be when X equals negative one y equals three and Z equals zero.

In probably 14. We want to solve this system of equations we have here three variables. Then we should eliminate one of the variables. That's it I. three. From equation to the equation We get equation three and multiply it By -4 and added to the equation one. Then We have 12. I won plus sorry it's minus four. Multiplied by four I wan. It's minus 16. I one plus two Gives -14. I wan -4, multiplied by six. i 2 gives -24. i two minus four -28. i two I four I three minus four. I three give zero finally equals 32 plus three, gives 35. And this is the equation four. We get the equation three and multiply it By two, then added to the equation two. Then We have eight. I won Plus two. I wan gives then I want We have 12. I too -4 i two. Is it a two minus two? I three plus two. I three give zero. Finally we have -16 minus 11 Gives -27. You can call it equation for it then we should eliminate I wan or I two to solve for one of them. We can get equation for and multiply it by 10 Divided by 14 and added equation 5 to eliminate. I want then we have minus then I want plus then I own gives zero, We have -28, deployed by 10 divided by 14 gives minus 20 plus eight gives -12 to equals 65 divided by 14. We have 75 divided by 2.2 by by 10 gives 25 -27 is -2. Then I too then I too must be 16 but there is a little mistake. Two multiplied by four plus three. Doesn't give 10 the strong, he's drunk and this factor is wrong. Let's revise it. We multiply equation three by two. Then we have four multiplied by two. We added 22 we added 23 years. Then it gives 11. I won and we have three multiplied Question three multiplied by two. Then we have six and employed by two games 12, 12 plus it is it. And we have minus Eight multiplied by two, gives -16 -11 gives -27. Then this is correct. That's true voice here and divided by 11. Sorry, multiplied by 11 divided by 14. Then this must get zero and of course these values are wrong. We have -28, multiplied by 11, divided by 14 Plus 20 gives -2. I two equals 35. Bye bye. 11 divided by 14 -27 gives one half. Then I too Equals -1 Quart. We can subside back in equation four. To get I wan then from four We have -14, I want -28 deployed by -1 quarter gives seven equal thirties five. Then I want equals 35 plus seven divided by 14. It's three but it's not 35 plus seven because this gives plus seven, 35 -7, divided by 14. Then I won equals two. Sorry again it's minus two because minus 14 Then it's -2. And to get I three We can substitute an equation number three here. Then from three We have four multiplied by Taiwan minus it Plus 6, 8 2, six month deployed by -1 quarter minus I three equals minus eight. Then eisley equals six, multiplied by -1, divided by four, which is minus three divided by two. And this is the final answers of our problem.

Here we have to solve the pair off. Linear equations given by three x minus off two Y is equal to three and two x plus off three by physical do minus 11. We can name them first and second equations. So murder playing first equation by and multiplying second equation By three we will get six x minus off four by physical dough six and 66 plus off. Nine way is equal to minus 33. We can name them third and fourth equation. So now we're subtracting 40 question from the herd and we will get here. Six. Sex will be concerned up and we were left with minus off. 13. By is equal do 39 or from here we will have via is equal to minus off three. Substituting bicycle to minus three into the 2nd 1st equation, we will get three into x minus. Off to into minus three is 1/4 3 We will have three X plus six is equal to three or three X will be quarto minus three. From the hair, we will have X is equal to minus one. So the values off X com. A viable big Quito minus one comma minus off three

The given question. He's ex my last three while plus two reality called 1 11 This is fast in question. Minus six plus four. White plus tree geological. Do find this second question to us minus two. Why minus four? Jail is according to this is interrogation. We have to add the first on dhe second aggression we get. Why bless Fine Jail is a 16. This becomes the fourth equation. Now reply the second equation. What do On DDE on aggression touch, we have minus two x plus eight way Last 16 isn't wanted. 10. This is one we obtained by multiplying the question. Second, with two on, we had adding Had a question which is Do I suffix minus two? Why minus four? There is 1/4 to Now we have to add this this calluses out This becomes plus six y glass. Dude, it is a quantum to elf. Then we have the fourth cushion on dhe. This becomes the field question. The 40 person is wide blast. Find it. Is it got to 16 on the 50 person is six wine. Bless. It was a dizzy Quentin to have women blindness integration with six on been advised this integration with one. We have six while plus strategy, it is equal to 96 on six. Why plus two days is 1/4 to 12 ever subjected? The questions begins. This cancels out. This is 20 and Jen is equal to 84. Therefore, Jen is equal to three, therefore, opens it now. Why, plus five days. A quart of 16. Why glass find into a tree? Is it for the 16? Therefore, why take 1 to 1? Therefore, why is equal to one on Jessica Tree now? Putting the value of y indeed an equation that's first. We have X minus three. Why? Plus two geopolitical to 11. It's minus three into why wine is one plus doing to trace the call to 11 x minus three plus 60 people. 11 It's plus Traci called 11. Therefore, X is going to eight. Hence, we obtained the village of sex as you come to gauge. Why is it going to one? And James is going to three? Is that the realism exploited? This is the final offensive


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