A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
how do i find a solution to a system of equations represented by a matrix?
anonymous
 one year ago
how do i find a solution to a system of equations represented by a matrix?

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well first you need to know how to read a matrix. Do you know how to read a matrix?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and im bad at asking for help

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438709526900:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay I'm just writing the problem here so I can see it more easier. And it's okay. I'll write how to solve the problem step by step. Just tell me when you are lost.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0itll help alot if i understand this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright I'll try the best I can in getting you to understand this. dw:1438709667710:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First you need to know how to read the matrix. As you can see there is a column name called x y and z. Those numbers below the variables are going to be part of the equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For example in the first row you see the numbers 1 2 and 2. When you put this into an equation you will use the variables above the first row to combine it as shown below:\[x+2y2z\]The 11 will be after the equals sign since that line separating 2 and 11 technically means equals. So now the equation will look like this:\[x+2y2z=11\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Did you get that so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, yeah okay i get it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since one would be just x, sorry takes me awhile to work things out.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's okay! Take your time! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know what the other two equations will be if you used my method that I showed you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great job! Now those three equations are needed when you are trying to solve equations within a matrix.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[x+2y2z=11\]\[5x+4y+7z=81\]\[4x+y6z=37\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now do you know how to solve for x's and y's?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0replace them with the numbers or..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not in this case since they didn't give us any numbers to put in for x y or z. So the first step is to pick any two sets of equations out of the three.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Let's start with the first two equations.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438710552563:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And it's okay. That was a rhetorical question.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait let me rewrite what I wrote on the side.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Pick which variable to make common. For example the y's can be made common by multiplying the 2y by 2 and leaving the 4y. When you multiply 2y by 2 you can get 4y. 4y and 4y equal each other so now you can subtract the whole equation to get rid of y.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Tell me if you get that part.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i do, but at the same time i guess i need to know why we are doing that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what is the reason for finding commons, is that like a big part of the equation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what is the end result supposed to be? like, is the Y now 1? bleh...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We are doing that so that we can get rid of one term and just concentrate on finding x and z. We will find y at the end.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why are we doing that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In order to find the solution to this matrix we need to find what x y and z equals. So we need to break it down by finding one variable at a time.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh alright. so whenever im doing this i have to find a way to get rid of a variable?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so, like in this equation for example: dw:1438711521979:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0they have to be in the same row to be able to get rid of them right? the 9 and 9 cant cancel each other out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry but where did 31 25 and 28 come from? It's the last column. And no you can't cancel out the 9 and 9 because one is a y and the other is a z. Remember the 2nd column are y's and the 3rd column are z's.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438711724574:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its an example problem of one i did and failed.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0totally different problem sorry just trying to see where this applies to other problems too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You understood more than before at least :) And oh ok. I'll help you out with those if you don't understand still.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you, youre a saint ;;

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay, so lets finish this problem first

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol you're welcome! And okay. We have one equation: 3x11z=59 after canceling the y. Now when you look at the 3 equations from earlier, you can see that we need an equation with just an x and z and no y but we don't have that. So we need to repeat the step in finding another 2 equations to cancel out y.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.03x11z=59 came from the drawing I drew earlier. Take a look at that and tell me if you get that.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0where did the other two come from?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It came from the three equations we wrote from the matrix.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438712602958:dw gosh im so sorry, im not sure where the two came from. i wrote down the equation again, to see if i can do what youre doing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0https://join.me/592430542 im sharing my screen with you, is that alright??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm pretty freaked out by that screen. Lol sorry but I don't feel like it's safe. No offense to you or anything. I just feel like it's a hack since that kind of screen popped up when my uncle's computer got hacked.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0pfft, im not trying to hack anyone and learn math at the same time but thats understandable. i usually use joinme with my friends when im drawin and stuff

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay. I'm really sorry about that! Are you able to draw here?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We're almost done anyways.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438713360885:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0alright, sorry i scared you haha

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the brushes on here kind of suck there for i kind of suck

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's okay you didn't know! :) And at least you draw better than me XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[x+2y2z=11\]\[5x+4y+7z=81\]\[4x+y6z=37\]*Just rewriting this so I don't have to keep scrolling up.*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i changed the background so its less menacing lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol okay. Now let's use the 1st and 3rd equations so we can get rid of y again.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438713734611:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438713838855:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438713940961:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What part did you get lost on?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438714161470:dw i dont understand any of it, how do we get to the answers that it wants, why am i so BAD at UNDERSTANDING THINGS

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh we didn't get to finding the answers yet. We needed to find two equations to find x and z. We did those last two steps to get rid of y.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why did we multiply that row by 2 though?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To get rid of the y. You need to multiply the equation by a certain number to cancel out the y. In that case the y in the 1st equation is 2 while the 3rd equation's y is 1. So if you were to just look at\[2y\]&\[y\]How would you be able to get that y to equal the 2y?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiply it by two but...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what happened to the row in the middle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh it was cancelled because we need to cancel out variables to find x or z. In order to find what x y and z equals we need to have two variables in two equations in order to solve it. That's why we got rid of y.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so...that whole row was canceled out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No just y was cancelled out. We subtracted the two equations to get rid of y and have only x and z left in a new equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im a kinesthetic learner, i figure things out differently im sorry this must be frustrating.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438715563780:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Did you understand this picture?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you know where I got the 1st and 3rd equations from?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets solve this whole thing and then break it down because i dont know where we are headed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay then hold on.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its really cool of you to help me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[x+2y2z=11\]\[5x+4y+7z=81\]\[4x+y6z=37\] 1st step:\[x+2y2z=11\]\[5x+4y+7z=81\] \[2(x+2y2z=11)\]\[5x+4y+7z=81\] \[2x+4y4z=22\]\[5x+4y+7z=81\] \[(2x+4y4z=22)\]minus \[(5x+4y+7z=81)\]equals\[(3x+0y11z=59)\]OR\[3x11z=59\](1st equation with no y's)  2nd step: (Pick another two sets of equations to cancel out y.)\[x+2y2z=11\]\[4x+y6z=37\]\[x+2y2z=11\]\[2(4x+y6z=37)\]\[x+2y2z=11\]\[8x+2y12z=74\]\[x+2y2z=11\]minus \[8x+2y12z=74\]equals\[9x+0y+10z=85\]OR\[9x+10z=85\](2nd equation with no y's) 

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And you're welcome! :) This doesn't give you the answers yet but I'm just going to show you this part to see if you understand it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You understand it now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay great! I should have just showed you the steps earlier like that lol. XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01st equation with no y's:\[3x11z=59\]2nd equation with no y's:\[9x+10z=85\]Now we need to get rid of x's in this step since that's the easiest to multiply with. We need to get 3x equal to 9x. We have to multiply the 1st equation with no y's by 3.\[3(3x11z=59)\]\[9x+10z=85\]\[9x33z=177\]\[9x+10z=85\]\[9x33z=177\]plus \[9x+10z=85\]equals\[0x23z=92\]OR\[23z=92\] Now that we have one variable left, we can finally find what z equals. Divide 92 by 23.\[z=\frac{ 92 }{ 23 }\]\[z=4\] After finding one variable, you can now substitute the z in the equation with no y's. You can do either the 1st or 2nd equation with no y's. It doesn't matter.\[9x+10z=85\]\[9x+10(4)=85\]\[9x+40=85\]\[9x=8540\]\[9x=45\]\[x=5\] Lastly we can solve for y by using the equations givin to us in the beginning of the question (from the matrices). Either 3 of the equations can work. Make sure to substitute the x and z.\[x+2y2z=11\]\[(5)+2y2(4)=11\]\[5+2y8=11\]\[2y3=11\]\[2y=11+3\]\[2y=14\]\[y=7\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Tell me if you understand that. This is the final step and it gives the answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ya it might look really long but don't let that scare you. Once you keep practicing it, it will be really easy! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0omg i actually understand

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yay that's great! :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0see, im taking a summer course and its online, the section imtaking is all about that so im stuck

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay. Well hopefully this was helpful in figuring out how to solve it. :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it was very helpful!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i might need help going through another problem because i know there are exceptions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438718495088:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay. If it's another problem can you write it in the Ask a question box? That way I can scroll through the steps that belong to that problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so do i get rid of the x?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0because 4 can go into the 8 or no

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438718635151:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ya you can get rid of the x or y since you can just multiply the 3rd equation with 4 so it can be the same x and y in the 2nd equation.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438718776581:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438718875081:dw