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X =1 X =2 X =3 Y =0 0.15 0.1 Y =1 0.1 0.05 0.25 Y =2 0.2 0.05 0.1...

Question

X =1 X =2 X =3 Y =0 0.15 0.1 Y =1 0.1 0.05 0.25 Y =2 0.2 0.05 0.1

X =1 X =2 X =3 Y =0 0.15 0.1 Y =1 0.1 0.05 0.25 Y =2 0.2 0.05 0.1



Answers

$y=\frac{2 x}{1+x^{2}}, \quad x=-2, \quad d x=0.1$

This system, you're gonna first want to get these equations that have decimal coefficients to the equation and Adric coefficients. And the way that you're gonna do that is you're gonna multiply by the smallest place values Dinamo batteries. Right, So this is tens, tens and units for the first equation. So you're gonna be a 10. You're gonna also everything by 10 that will move the decimal place one to the right on all your terms. So under the right one to the right, of course, one of the right. So you end up getting is two acts minus one. Why is equal to can? Okay, on the other equation, you're gonna multiply the entire equation by 100 because you have a tense hundreds and hundreds, so it to get rid of all the decimals, you gonna multiply by 100 K So what you have here is moving in to do the right to the right. To the right. I mean alternative move. That's all. Thanks to to the right is your times in the entire equation by hot. So you end up getting 10 X minus 13. Why is equal Teoh? So here you have your two of Covalin equations with indigent coefficients, which are much easier to work with. Okay. All right, so then you're gonna take these two equations and ask yourself, we have to get one of the values of their extra wide by itself traffic at which of those values you're gonna work with to get by itself. And it looks to me like the easiest one saw is gonna be for why on the first equation? Because if you look at you got the coefficient of y being a negative one makes it very easy. Stall for a while so you can pick either equation extra wide. It's all for I chose the first operation, and we're gonna solve for a while. Okay, Once we have that, you're going Teoh right down here. So you get to X minus one. Why is he put the time you want to get the Why by itself. So you're gonna add white of both sides, and then if you're gonna bring the wives to the right, you undo the plus tens or minus tend to both sides and you're gonna end up with two. X minus 10 is equal to y. And so that's the same as why is able to do X minus 10 once you have. Why, in terms of X, you can then take this equation here and the expression for why is two x last time? You can then substitute that in for the Y value in the second equation and you set number two. So let's do that. You're going to get 10 times X minus 13 times, whatever wise. And we said that Why? What is going to be two x minus? Tan close pregnancies are gonna set that equal. Teoh, can I solve this like normal? And this is going to give you the explication of the intersection or the ex part of the order pair. That is the solution of the system. And when we saw this, we're gonna just kind of go through and, like, normal, So 10 access comes down and then six down and then most quiet two x my standby negative. 13 says tribute to the prophecies. Negative. 13 times positive to access. Negative. 26 x negative. 13 times a negative. 10 is a positive 130. That's gotta be equal to two. And then you're going to combine your light terms. So 10 X minus 26 X It's going to be negative. 16 access and you're gonna have a plus 1 30 coming down just like it is Nazi. Put a chip. Your goal is to get the excess by themselves. You want to get rid of this? Plus 130 sugar on my ass. 130 of both sides. And what you're going to get is you're gonna have negative 16 axes is equal to negative. 128 now, when you have negative 16 X equals negative 1 28 us all for the value. One X You have to undo multiplication with divisions. You're gonna divide both sides by negative 16. Prohibition of acts. They're going X is equal to negative. Divided by a negative is a positive. 16 times two is 32 that double B 64 $64. We won 28 right, so it looks like two to get to 3 to 4 to get to 64. And that eight will get you to 1 28 So it's gonna be eight. So there's your answer. X is equal to eight, which means that the order pair that's the solution of the system is eight comments, something we don't know what the Y value is yet you're then going to take Let's do this in Iraq. You're going to then take the original equation here that we solve for why? And we're going to plug into that with the X value we have. And see if you figure out the y value that goes with it. So why is now equal to two times whatever? Exes Minus ter two times 8 16 16 miles, 10 to 6. So it looks like your order pair. That's a solution. The system is the word. Pair eight, Common six X value eight white. Come on, Sex. My value 60 Tuesday. So what we're gonna do now is we're gonna check this to make sure this new still in the states some of the grab different color here will be a little check. We're gonna take this order, pair. We're gonna play it into the other original creation that we haven't used really much. This one right here on this outside, right. We're gonna plug in and see if we get you statement. So here's our check to see if we got a true statement. Is it true that 0.1 times eight minus 0.13 times six is equal to 0.2? Is this a true statement? Well, 0.1 times eight is gonna be a zero point and 0.13 times six is going to be basically 13 times six. This is gonna be 60 plus 18 or 78. But it's gonna have this will to do the right to the left. So V 0.78 So you get a 0.8 takeaways here about 78 And is that people 0.2? The answer is yes. So we know he got it right.

Common salt in the system. We've got decimal coefficients. Easiest way to get a dismal coefficients is just to multiply the entire equation by the denominator of the smallest place value. Basically, right. So we got tense, tense, intense, most by the whole thing for the 1st 1 And that just moved that. That's from one place to the rights whose becomes two x minus y equals one. And then the other one, we want you both. Bye bye. Got hundreds and hundreds and hundreds. Some off by 100. She almost by the whole thing by 100. And that means they're gonna move the decimal place to to the right. You get one X and then plus for why is equal to 23. Okay, so now that we have are easy a couple in equations, we're gonna do Step one, which is get other extra wide by itself, neither equation. This is obviously the one that makes the mother sense, because you got a positive one ax. So let's just solve for X. There we get X is equal her. It's not skip steps for you guys much. Everything's here. So ax plus for why is equal to 23. We're gonna take away for a wife from both sides, and you're going to see that? The answer There is an excess equal to negative for a while, plus 23. Once you have the X value in terms of why you can then take that and you can substitute it into the other original equation. So I'm gonna use the modified version here. And look, we're gonna place the X right there with the new value of X that we have and two step two. So we've got two times. Whatever X is out was acts was negative for y plus 23. And then we're going to add or take away from that one way. I'm not sure. Vehicle the one so you can distribute through the parentheses here. And when you destroy it through the front, sees you get negative. Eight. Why? Because two times negative force. Negative eight and two times positive. 23 is positive. 46 tnegative eight y plus 46 minus one. Why is equal to one? Do they want to combine your like terms here? So negative eight y and they one wire together. It's negative. Nine wires she had negative nine. Why plus 46 is the one you want to get the negative nine wives by themselves. How do you under plus 46 minus 46. Not to one side, but both sides. And you get negative. Nine. Why people should negative 45. You want the value of one wise. So how do you undo times by negative nine divided by Make it mine both sides of your equation and you get why is able to negative 45 Delighted by negative nine, which is positive. Five. So you think that the order pair solution is gonna be some value of X that we don't know yet. And if I for what? But now we gotta figure out the X money that goes with that. My value of five. So they were going to take the once bigoted and colors dio or injure. We're gonna take the y value, plug it into this great in here that we've already some facts and figure out the X that goes with the while. So X is equal to negative four times. Whatever the Y value. The intersection is shopping 35 and then plus 23 Well, that's gonna be able to see a negative 20 plus 23 which means that the axe value would be three. So you think the order pair? That's the solution to this system. Is there a pair of three common five? We want to be 100% sure. Everyone making still in the stakes, so we're gonna check it. So I picked red is my check color, and we do a little checking red just to make sure we didn't make a boo boo. I don't think this order pair. We're gonna plug it into this original equation with decimals. We're going to see if we got the right answer. Okay, so we have 0.2 times. Well, I guess, technically, yeah, I say that when a special appointment. 0.2 times three minus 0.1. Times five should be closer. Appoint one. Let's see if it iss There are plenty of times three is 0.6. And that you disappoint one times five is gonna be negative. 0.5. Is that equal to a positive 0.1? Yes, it iss. So we verified that the correct answer is to become a five, actually, 315 That's a solution to the system because it's a solution or repair that exists on both of the lots. It's a place to intersection.

Building the system. You're gonna want to rewrite these equations with metric coefficients. The easiest way to do that is to multiply by the smallest place values the nominator. So the first equation here, we're gonna both fired by 10. That basically means you're gonna just move the desolate place. One place to the right, Uh, in all the terms in the equation. OK? All right. That's yes. And see, you must buy the whole entire equation by 10. And you're gonna get one X Plus five. Why is equal to for on the other equation over here, you're gonna let supplied by the smallest place value denominator, these air 100th. So you're gonna move by the whole thing by 100. So we're gonna move the decimal place two places to the right. And so what you get here is negative. Three acts plus one, why is equal to 20? So now you have your equivalent equations. You're gonna go through the process like normal jig in that city. Step one wishes to get either the extra wide by itself in either equation makes most sense to use this equation the left, because we already have X by itself basically one X anyways, so that is Get rid of this plus five. Wife is process to go through. So we have X plus five y is equal to four you want to solve for X. They're going to take away five y from both sides and we're done with that. You're going to get access equal to negative. I have. Why? Plus four, Once you have an expression for X in terms of why you're gonna take that and they're gonna replace the X in the second equation with that value. So let's do that. And what we're gonna get here is we're gonna get negative three times, whatever access. And I said that X was negative five y plus for and we're going. Teoh had wind of that and get a value of 20. And so now we're gonna multiply through by the negative three negative. Three times a negative five wise positive 15. Why negative. Three times a positive for is a negative 12. We're gonna add wide of that. You get that equals 20 combining like terms 15 wide plus one. Why is 16 why? And so you get 16 y minus 12 is equal to 20. How do you under minus 12 involved? Besides your equation. So what you're going to get there is 16. Wise is not equal to 32. How do you undo times by 16 provided by 16 both sides. And so what you get for a while? Value is to. So you think that the order pair that is a solution of the system's gonna have a two For why? We're gonna figure out what the X value is. So now we're gonna take that. Why value to we're gonna place it with into this equation. Here we were myself. Racks. We're gonna figure out the exercise that goes with it. So let's do that. X equals negative five times. Whatever. The wise to plus four. That means that X is gonna be equal to negative 10 plus for just negative sex. So it looks like the X value is going to be negative. Sex on the Y values get a positive too. We're pretty sure this is the right answer, but we did check it. So the check it, you take that X and y value. That's the order. Pair of the solution of the system. The point of intersection between two lines. We played into this highlight of yellow equation. Really? So now to check it, we're gonna plug into this other original operation of your give to make sure it's a solution with not just one of the equations, but both We do that we're gonna do it into the original. So what you get here is you get negative 0.3 plans whenever access negative sex plus 0.1 times whatever wise to and that should be equal to 0.2 negative 0.3 or three hundreds times six is gonna be negative. 0.18 are shy. Positive zero. But money is negative and they gave us a positive and 0.1 times two is gonna be just double 0.1 nb 0.2 Now we're gonna ask, Is that equal 2.2? Well, if we add 18 hundreds plus two hundreds, you do get 20 hundreds, which is the same as 2 10 So it it. So we know that the answer negative six comments to is the correct order pair and it's the intersection point between the lines and specialises

The question is to find Philip glass fronts from on the given day in every patient ex dish minus x minus y else who won. Ah, exact zero plus one Electric wants to question Second is minus X plus y dash minus y equals +20 y act zero equals from minus five by No, I like the second equation. No taking the loved us transform off equation first big s X minus minus x zero minus Except this minus y s equals toe one upon us. Now, as we know, that exact zero is one for preventive value as minus one minus x miss minus Y s. It was from one of on s now taking az minus one s Coleman X s minus. Why, yes, exactly. Zero is zero slickly re Tzeitel, which is a close one upon this. Like with 30 question now taking the love last transform of second equation, We get X. Yes, bless s why this minus. Why zero minus y as it was. Zero s minus one mu. I s minus X. Yes. Equals minus five. By that is thanks s equals. Who s minus one? Why s plus five? By not putting the value off fourth equation and 30 question we get s minus one s minus one. Why s less? Five by so minus Y s was one upon us. AZ minus for oneness. Quit. Why is unless I s minus one foreign spoof minus by s equals one upon S. NEC Will We were us minus one. This square minus one Y s. It was from one of on us minus five s minus one On whom that is s s minus two Y y s. It was toe who minus a rest fled. Bless by rest, that's I rest upon the Wisc. That s why else would make whereto minus my races were less by rest on. You will, Yes, yes, as my nest. So using the partial fraction wise would be minus one important who was square minus three upon to west minus one of honest minus. Who taken the inverse love Last variety would be minus the upon toe minus Terry upon minus ear is to the park to be now the equation second becomes X he less minus one upon minus. The weed is too divided to be minus day by U minus three like minus years to the park. Poopy people stew Zero That is next team with vapor toe being upon to minus serious Barghouti, less one. So the final answer would be X'd was to being upon to minus cedars. Barto less one and variety equals two minus steel by two minus revive. Toe my ass. Ears to pacto. Thank you.


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