solve-each-system-beginarrayl2-x-4-y6-z12-6-x-12-y18-z36-x2-y-3-z-6endarray

Question

Solve each system.

$$\begin{array}{l}2 x-4 y+6 z=12 \6 x-12 y+18 z=36 \-x+2 y-3 z=-6\end{array}$$

Jake Zanazzi · Accepted Answer

but the system is two x minus four y close six z equals 12 six x minus 12 y e t z equals 36 and negative acts close to Why, yes. Three. The equals negative. Six. So what you could notice about these equations is they&#x27;re all multiples of each other. Two times 36 Negative. Four times negative three times three is now 12 6 times Stories 18 12 times three is 36 negative one times native sixes 62 times negative. Six is next 12? Make it three times negative. Six is 18 negative six times negative. Six is 36. This means that they&#x27;re gonna infinitely many solutions, right? Because any solutions to this first equation is also going to satisfy the second and third equation, since they&#x27;re just multiples of each other. Um, so actually find one solution if you ask to, um, you might be asked if they&#x27;re infinitely many solutions Final One because not any X y and Z is going to solve this. But I think you just plug in zero for X and Y or for y and Z and then solve for the third variable. So if you plug in zero fraction Why you get 60 equals 12 z&#x27;s got equal to. So you know, zero you&#x27;re too. Is an example of the solution. Um, and then just plug. Listen to double check. Six z is 12 that works. 18 z equals 36 That works negative. Three z equals negative. Six that works. So there you found your infinitely many solutions to this.

Louisa Benatovich · Answer

So here we&#x27;ve got a system of three infections with three variables as it goes, Why X? And we&#x27;re trying to figure out what each of these is equal to. First step. Choose a variable that we want to cancel. Well, when you look at these three columns of variables, looks like the X is going to be easiest. You can already see the three and the negative three. That&#x27;s how you do math strategizing. So now that we&#x27;ve chosen our victim, variable, you look at these three equations, we choose which ones we want to add together first. Well, like we said, we got the three and the negative three. So how about we try adding these two together first? Because we know we won&#x27;t have to do and multiplication. So let&#x27;s rewrite thumb the X plus for why minus three times three 6 12 c. Perfect. We&#x27;re adding them together. No multiplication necessary. Please cancel as we wanted them to for why minus six wives negative two y. This is a positive 40 is too perfect. We&#x27;ll save this for later. Got a two variable equation going back to the top. We need to pick two other equations that together How about the 1st 1 and the last one? Go down or rewrite? Um, we&#x27;ve got six X plus two y plus four easy. It was to negative three X minus six. Why class 12 0 people&#x27;s five. And what can we do to the bottom equation? To get it to cancel the top equation? Well, we&#x27;ve got six x here, and we have negative three X here. What can we do to get this to negative six x? You guessed it. It are multiplying by just a regular old, too. So when we re write this, get negative six sex perfect battle. Cancel minus 12 Y plus 24 g. Perfect. Now this is gone. Imagine this completely gone, and we&#x27;ll just add this top to the bottom. So put a big plus sign there. All right, six x minus six x, but cancels zero Exactly what we wanted. Do I minus 12. Why is negative? 10. Four Zia plus 24 0 28 z and then to just 10 minutes. Perfect. We&#x27;ll save this for later. So we&#x27;ll go back and look at the top. Are other equation with two variables negative. Two y plus four. Z equals two will write it down here. Negative. Teoh plus four z equals two. So we need to add these together to cancel them somehow. And here it&#x27;s pretty complicated already. So you think this pick either variable? How about we go with the why? What killing? Multiply this by to get it to cancel. Negative 10. Why? Well, we would need it to be a positive 10 right? So what do you multiply? Negative to buy to get a positive 10? Yes, it&#x27;s a negative. Five negative times. A negative is a positive. So we multiply both sides by negative five. Where do you get a positive 10? You get enough in 2010. So this is gone because we have the new and improved version of it. You don&#x27;t usually have to cross the night. I just do that so that you don&#x27;t get confused. I got him a big, big plus sign cause we&#x27;re add even together. So what happens when we adding together? All the Thames can see just that We wanted them to This becomes a Z and then this 12 minus 10 becomes too well. This is interesting to get Z by itself. We divide by eight on both sides. Is he going to over eight? That&#x27;s a fraction. Remember to always simplify the fraction because we can divide both the top and the bottom by two. It becomes one for so easy is 1/4. We have 1/3 of the puzzle finished. So let&#x27;s look back to one of our two variable equations. How about negative 10? Why plus 28 z? People swell because we know what Z is. We can plug it into this equation right here and then sold for a while. All right, so let&#x27;s plug it in. 10. They get 10. Why? Plus 28 times 1/4 equals 12. What&#x27;s 28 times 1/4 It&#x27;s seven. Seven equals 12. You keep going down solving? Sure. Why not get a 10? Why equals five and then you devised by 10 on both sides using your algebra brains? Why equals negative 1/2? Because you&#x27;re simplifying this perfect Z equals 1/4 y equals 1/2. We only have to figure out X. Let&#x27;s go back to the beginning and choose one of our regular old equations. How a bout Negative three x minus six y plus 12 z equals five. It doesn&#x27;t really matter which one you choose. They&#x27;ll all work, so we don&#x27;t know what accessible. Leave that minus six times Why? Which is negative. 1/2 was 12 times Z, which is 1/4 here. There once he is 1/4 wise. 1/2 equals five soldiers. A multiplication negative three x is the same negative six times negative 1/2 is a positive three. 12 times 1/4 is also three equals five. That&#x27;s the same as saying Negative three X plus six. Those add together people&#x27;s fine. Subtract the six over negative one. Divide both sides by negative three. Remember that the negatives air going to cancel So you get X equals 1/3. It causes 1/3. So you did it executes 1/3 z equals 1/4 y equals negative With that nice work

Vikash Ranjan · Answer

The event in question is eggs plus six days in front of 12. This is fast ignition minus two X plus three, while is equal to six. This is second equation. And why minus upon to firebomb to desist? No, but exit a quantum 12 minus 68 in increase in second that they just gives us finest doing dupe. Yeah, minus six years plus three by six, minus 20 for less who objected less. I see why you&#x27;re under six. Therefore three. Why? Plus two injured. She will do six plus credit for Why? Bless for dead, is it Waldo? Damn, this is the fourth question on. And the question is why minus deal upon to and you could file a pawn two, which is to y minus state, as it will do file dis aggression. That is a question three on DDE we have. Why less or did is he got a den? This is aggression four. No, we have to do the operation. Jeez, Abdomen obliged. Execution by two and applied this equation. But well, the skips do I minus stage people five. And so why less? Where is he going? Toe 20 Never subject destitution. It&#x27;s against us. Out. This is minus nine. Jane is equal. Dough minus 15. There are two dead people. Do 50 minutes on nine, which is fire. Bunty, since that is known therefore, why bless for there is equal to them. Why bless four into? I went crazy with them. Why? Bless 20 country and you got it. Jen, why is it going to 10? Minus 20 upon three, which is even tow 10 upon three. Therefore Y is equal to dinner for three on Dhe. Therefore, you&#x27;re dizzy. Puerto Five. Since we have the village off. Why on Jade therefore, make an imprint of his offense, which is Texas Tickle toe. Well, my last six state that is equal 12 minus six in tow. In a country to see for 12 minus 20 does isn&#x27;t sonny. This is 513 It gives us This is Well, um I understand. It is toe hands. We have gender values of X is equal to two. Viatical to 10 upon three and there is going to find country. This is the finest

Rebecca Polasek · Answer

to solve the system of equations. And I have three equations with three variables, So my ankle would be to cancel out one of the variables. And as I&#x27;m looking my equations here, I noticed that actually could use why to eliminate. So let&#x27;s use the 1st 2 equations to eliminate why and notice that they&#x27;re ready to go. Plus why, and minus why are gonna cancel out. So we have negative two X class y minus three z equals six and then the second equation for X minus y plus Z equals two. Those were good to go. Let&#x27;s go ahead and add them together. So we get a positive two x, the wise you&#x27;re gonna cancel. We get a minus two Z in a sequel to eight. Let&#x27;s go ahead and pause right there and try and eliminate again. Since we have enough equations, we can actually do it again with a new pair. And then, based on whatever&#x27;s left behind, we can see where to solve from there. So I&#x27;m gonna use the first and the third equation now to eliminate cause again, I noticed that the wise are ready to cancel out. So negative two x plus y minus three z equals six and then the third equation two x minus y plus three z equals one. So as I put these together negative two x cancels out with two x. Why cancels out with negative? Why negative three z cancels out with three Z so there&#x27;s only zero left on the right side and six plus one makes seven. Does zero equal seven? No, this is false. So if you end up getting a false statement so something that&#x27;s not true, like zero equal to seven, then we say this isn&#x27;t no solution.

Adam Dehollander · Answer

in this part, we see that we can solve to get why in terms of sea and we can start to get excellent terms at sea and said that if we do that, we can like everything into the top equation and get in it Asian on Lee in terms of C. So let&#x27;s do that. That&#x27;s first so far. Why in our second equation? So if we add, see over six to both sides and then what about a boy that would give us why? Is equal to 2/3 I&#x27;m see? And now in our that equation, if we add Zito both sides and then divide by two that gives us the axe is equal to connected to divide back to its nectar one. And then we have passed of Shia Divide by two another. Which one is she? And so now we have X and y in terms of sea, so it&#x27;s like that into a tap equation. So six times acts is six. I&#x27;m snake. Give one us 1/2. See, that&#x27;s why just to see minus four C is equal connective. So that&#x27;s combine that Z terms. We have a 1/2 see Time&#x27;s a 60 is who we see. And then if we subtract, it was easy. That is negative one. See, we still have a tooth. Didn&#x27;t see right here. And then with that Constance, we have a negative six on this side. So when we add that to the right side of the equation, that leaves us with negative too. And so now if we do a negative Z 1st 2/3 E, that leaves us a negative one thingy. It&#x27;s equal connective too. And if we want both sides of the equation by negative three and gives us then CIA secret sex And so now we have one of the variable soft boy we can plug that into this equation to Third Z is equal to why two things Time six we can do six divided by three is two times two. So why a secret for? And then we just have one more beer but herself for that specs. So we see that the excess negative one plus 1/2 see so that 1/2 see is 1/2 time sex with three D Answer three plus negative one. It&#x27;s true. Xs equal to high secret of four and CIA secrets

Jake Zanazzi · Answer

All right, so we have to acts. Minus why? For 62 y z equals negative. Four and eight X equals three. So that statement stared equation. And we just solved for acts that people three divided by eight. You can play that up in, appear to solve. For a while, we would have six divided I eat minus lie equal. Six So wise. Gonna equal 6/8, minus six. Uh, because you can just move the Y over the right side of the equation and the six over the left side. This is going to give you, um, negative 21 about about four, and then even solve for Z right here. So to in a 21 out of the floor. Excuse me. Let&#x27;s see. It was negative before I mean the negative for cute. About about four ounces. He was negative. Four. And then, if you take a negative four and add, um 42 divided by four, you&#x27;re gonna get 6.5. Now we have our X y Z people&#x27;s three days. You&#x27;re going one about four and 32. You can double check for these. Make sense to come. Zach. Six seats minus y minus negative. Going one about before equal 62 Y Posey will equal Negative four and eight x William All three.

Problem

Solve each system. $$\begin{aligned}3 x-y+z &=5 \…

Problem 35 Medium Difficulty

Solve each system.

$$\begin{array}{l}2 x-4 y+6 z=12 \\6 x-12 y+18 z=36 \\-x+2 y-3 z=-6\end{array}$$

Answer

$\{(x, y, z) \mid-x+2 y-3 z=-6\}$

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$\{(x, y, z) \mid-x+2 y-3 z=-6\}$

Algebra for College Students

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Solving Absolute Value Inequalities

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Mark DugopolskiAlgebra for College Students

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