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As BA denned . ExplamSolve the following linear equation systemHJLA] [H...

Question

As BA denned . ExplamSolve the following linear equation systemHJLA] [H

As BA denned . Explam Solve the following linear equation system HJLA] [H



Answers

Find a linear function $h$ given $h(-3)=3$ and $h(0)=2 .$ Then find $h(-6)$

So we're gonna use a linear combinations to solve a system of Olynyk a linear region. At first glance, you might find this problem to seem overwhelming because the very first thing that you see is a fraction. But on the bright side, H here has a coefficient of one, and down here it has accomplished another negative one. If you like, you could, you're ready to eliminate variable here by adding the presence because each plus negative h would be zero. Which means the first thing I'm really adding is one half G plus negative one g. No, I know that that's gonna be something G. And so what I might do off to the side give myself a little bit of space to add the coefficients of one half and negative one one hand bus. Negative one. But I would have to put over one. I need a common denominator. So one half plus multiplied top and bottom by two because every due to the bottom through the top. And that would give us a negative one half so negative one half a T equals Remember, age disappeared because H plus negative age is gone. Two plus two would be four and to get to you by itself, multiplied by the reciprocal, which is negative to over one or just negative, too. She's no by itself because he's canceled and so G would equal four times. Negative. Two is negative. So I have half of my answer, which would be whatever the coordinates to you would be so that negatively. No, I still need my age. Coordinate. So what I might do is actually put it in this one. Even those a fraction looks a little simpler because it doesn't have as many negatives going on in it. But it's your preference if you prefer to. The old negatives go for it for deal. Fractions of the negatives go for the top one, do half of G, but he is negative. Eight plus h equals two. So half of negativity is negative for plus H people's, too. To get rid of a negative four, I would add it because negative four plus four is Europe. Whatever doing once other, doing the other insists things that h would equal six. And so that's my second important

In this fusion, the given system of equations are that is first question is given W H is equal to nine means product of WH. W and heads is equal to nine. And second is equation given that is the blue plus edge is equal to six. Now in the fusion, it is saying that we have to solve this system of equations. Educations by Algeria. Weekly. Yeah, so let's start for in the execution a step by step. So first I will write the given equation again. That is first equation is W. H is equal to nine. And second question is the blue plus edge is cool to six. No, I'm giving the numbering to both equations. So I can say that this is the equation number one and this is this is the equation number two. No, my next step is we have to solve this system of equations by algae epically. So here I am playing method called the substitution method. So according to this question I will get the value of edge in term of W. So after it I will put this value of edge in another equation. So No, for finding the value of age. In terms of the blue, I will use the equation number two that is W plus edges closer to six. So simplify it. Then I will become that is equal to six months to blow. So I can say that the ads which I get is in term of the blue that is equal to six minutes to blue. So no use this value of edge for replacing in equation number one. So it means substitute H is co 26 minus W. In equation number one. So after some shooting that it will be written as that is wh w will be W and H is that is multiplied by H is that is six managed to blue is equal to nine. No simplify it by removing parenthesis. So I can say that six W result will be 36 of blue. Six W minus The Blue Square is 4- nine. No next step is subject 9 to both sides. Then it will be bitterness. The result will be that is six W minus w squared minus nine is called 20 No, actually step is marty play negative sign to both sides. So reserve will be witness. That is a question which I get in result. That is equal to W is choir minus six. W plus nine is 4 to 0. So the result in which the equation which I get in result is in quadratic forum. So no, my next step is we have to solve er this credit equation. So so I can say that this left side, the left side, the term will be written as that is W minus three Holy square and is equal to zero because as we know the Pamela of a minus B is equal to a squared plus b squared minus to a B. So against it The Blue -3 holy square will become duties the blue square plus nine minus six to go. So I can say that this is equal to a website of this credit education. So it will become that is in the result that is W monastery Holy Square is equal to zero. So simplify it. Then I will get the value of W. That is equal to three. No I have to find the value of edge. So I will use the equation number To that is the blue plus edge is called to six. So write this equation number two again that is W plus ages 4 to 6. Now substitute the W. Which I get that is equal to three in this equation # two. Yeah so after some shooting it will be written as that that is the blue will be released three. Plus edge is equal to six. So simplify it. Then I will get the value of H that is equal to three. So now I had to get the variable of, sorry I had to get the value of W. Variable and that variable. So it means I had to get the solutions of human system of equations. That is solution is W is equal to three and edges can do three. So this is the answer of given occasion. Thank you.

So we're gonna use linear combinations to solve the system of linear equations. So the first thing that I wanna dio before I worry about the decimals is just to get everything lined up. And so I noticed that this bottom equation is actually in standard form. It just kind of looks little backwards. It says 3.6 equals negative point to G plus h. So I'm just actually gonna rewrite that over here, But I'm just gonna swap so it's gonna say negative point to G plus h equals 3.6 and then we'll decide if we have to change that at all. So I want to get this quake is in the same format, which means that to do that, I would subtract 4.3 from both sides. And so if I do that, it would say 0.1 g minus h equals negative 4.3. And again, the reason it's negative 4.3 is because we're subtracting 4.3 to come to the other side. And so now my GSR on top of G s H is on top of ages and my constant on top of constants and my equal sign on top of equal signs. And the nice thing is that in once thes two equations air lined up my coefficients of HR opposites. I've got negative one on one. So I'm actually ready. Thio ad. I'm gonna add my equations together. And so I've got one G plus negative point to G, which would be negative 0.1 g negative h plus h would be zeroes that's gone equals And then negative 4.3 plus 3.6 would be negative 0.7 and so on. My next step would be to divide both sides by negative 0.1, and so I would get G equals. Now it's gonna be positive because the negative divided by negative is a positive. And one thing that I could do here is I could just move my decimal over one place, top and bottom, whatever I do the bottom I do the top and I would get 7/1, which would be seven. So my G value would be seven. And I'm looking for a G h value in order to pair. So I'm still looking for that missing H. And so what I could do is I could go ahead and plug that into maybe this bottom equation. And so I would get 3.6 equals negative point to times seven plus H. So 3.6 equals negative 1.4 because a negative times a positive is a negative. Seven times two is 14 with one decimal place plus h. Then I would add 14 to both sides and each would equal 50 or five, and so my solution to this system would be 75

So we have a is equal to 1/2 B h. Which means sometimes we thought of his area equals 1/2 base times height. But for us, we're just these variables, right? So and we're solving this thing for four h. Okay, well, so the first thing I see each is over here, right? And I see this fraction in front. So let's get rid of this fraction. First of what I want to do is multiply both sides by two of the most. If I multiply the right side by too well, 1/2 times two is just one is gonna cancel out the 1/2 and get that two times a is just equal to b times H or to a is equal to B H. Now we're solving this thing for H so econs divide through by the coefficient in front of the H or the be. So we get that age is just equal to to a they provided by be so h two a over B. Um, you couldn't write this as you know, I guess you could say no one over B times to a, um would be the same thing, right. But typically would just say to a over B, um is equal. H I think you're


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