A community for students.
Here's the question you clicked on:
 0 viewing
gdogthegirl
 2 years ago
Ok i have to solve this equation by using elimination and the steps are
gdogthegirl
 2 years ago
Ok i have to solve this equation by using elimination and the steps are

This Question is Closed

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0Step 1: Identify or Create Opposite Coefficients Step 2: Identify or Create Opposite Coefficients AGAIN Step 3: Solve the New System Step 4: Substitute and Solve I got to step number 3 and then got stuck... Here are the equations x2y4z=10 2x+y+2z=1 3x3y2z=1 Step 1: (2x+y+2z=5) +(3x3y2z=1) which then equals 5x+y=6 simplified Step 2: x2y4z=10 2(2x+y+2z=5) (x2y4z=10) +(4x+2y+4z=10) and then i got stuck because now there is two opposite coefficients

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2in STEP 1, what is y3y ??

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0oh i ment to type 2y i had a mess of my notes/work

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0okay than what next

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2now ADD (x2y4z=10) +(4x+2y+4z=10) what u get ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2oh wait, how did u get 10 ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2it shouls be 2, isn't it ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2(x2y4z=10) +(4x+2y+4z=2)

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0you have to make another set of coefficients by modifying the problem so i times 2 by the equation 2x+y+2z=5

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0and i tryed not timeing it by two but the variables missing have to be the same in both equations

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2wait, where did u get 5 from ? isn't that 1 in original question ?

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0yes because it shows that you have to like jump from step to step i included the steps up there hold on a sec i will try copying and pasting the example

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2wait, i will write first 2 steps , u check

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0here is the example problem x + 2y – z=–3 2x – 2y + 2z = 8 2x – y + 3z = 9 Step 1: Identify or Create Opposite Coefficients Identify or create opposite coefficients in two of the equations and add them vertically. Recall that opposite coefficients allow you to eliminate variables since they have a sum of zero. Do you see any opposite coefficients? Look at the first and second equations. There is a pair of opposite coefficients in 2y and –2y. Let’s add the first and second equations. x + 2y – z=–3 + 2x – 2y + 2z = 8 3x + 0y + z = 5 which simplifies to… 3x + z = 5 Unfortunately, you can’t find the value of one variable yet. Put this new equation off to the side for now, and move on to the next step. Step 2: Identify or Create Opposite Coefficients AGAIN This step is incredibly important! In this step, you must eliminate y again by combining two equations. But this time, you must use the equation you didn’t use in step 1. In the first and third equations, the y terms have opposite signs. So these two equations are a good choice for elimination. Multiply each term of the third equation by 2. x + 2y – z = –3 x + 2y – z = –3 2(2x – y + 3z) = 9 4x – 2y + 6z = 18 Now add the two equations. x + 2y – z=–3 + 4x – 2y + 6z = 18 5x + 0y + 5z = 15 which simplifies to…5x + 5z = 15 Again, you're left with an equation with two variables instead of one. But if you go back to the new equation from Step 1, you have two equations with the same two variables. You know how to take care of that! Step 3: Solve the New System A new system of equations, with only two variables, has been created by eliminating y in Steps 1 and 2. 3x + z=5 5x + 5z = 15 Now this looks familiar! You can solve this system of equations using the elimination or substitution method. The substitution method looks easier since z in the first equation has a coefficient of 1. Isolate the z variable in the first equation. 3x + z =5 –3x –3x z = –3x + 5 Substitute –3x + 5 for z in the equation 5x + 5z = 15 and solve for x. 5x + 5z=15 5x + 5(–3x + 5) = 15 5x – 15x + 25 = 15 –10x + 25 = 15 –25 –25 –10x = –10 x = 1 Substitute the value of x into one of the equations and solve for z. 3x + z=5 3(1) + z = 5 3 + z = 5 –3 –3 z = 2 Now you know that x = 1 and z = 2. Two variables down, one to go! Step 4: Substitute and Solve Substitute x = 1 and z = 2 into one of the original equations and solve for the remaining variable (y). Write the solution as an ordered triple. Solve for y when x = 1 and z = 2. x + 2y – z=–3 (1) + 2y – (2) = –3 1 + 2y – 2 = –3 –1 + 2y = –3 +1 +1 2y = –2 y = –1 Since x = 1, y = –1 and z = 2, the solution is (1, –1, 2). Graphically, this represents the only point where the three planes intersect.

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0it is super confusing to me

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2i will write step 1 and 2 ,see whether it make sense.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2STEP 1: ADD 2x+y+2z=1 +3x3y2z=1 __________ 5x 2y +0 =2 so 5x2y=2 >(1) STEP 2: multiply 2 to 2x+y+2z=1 > 4x+2y+4z=2 ADD : x2y4z=10 +4x+2y+4z=2 ___________ 5x +0+0=8>(2) GOT THESE STEPS ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2now from (2) u directly have 5x=8 so x= (8/5) ok ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2now since u have x, from (1) can u find y ??

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0not really i don't understand how i can get y when i only know one variable and there is three variables because in the example it shows step 2 turning into another equation

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2no! in (1) u only have x and y and u got value of x..... 5x2y=2 put x= 8/5 here ^

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0oh ok so 5(8/5)2y=2 and y = 5

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0and then you would substitute those into one of the original equations right?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2thats right! y=5 :) yes, now u have x and y substitute in any of the original equation, u will get z ...

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0(8/5)2(5)4z=10 i get x=22/5 is that right????

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0i went to go put those into the practice and the fraction 8/5 won't even fit... im in the practice part of the lesson and i couldn't figure that out and you can put your answers in and then it will tell if it is wrong or not but i can't even put the fraction in it

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2z is actually, 23/5=4.6 x= 8/5=1.6 try putting 1.6,5,4.6

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0i was on the wrong practice problem duh sorry my brain got all confused with all this thank you so much for all your help :)))))

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2lol! its ok. but did u understand the process ?

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0yeha i mainly got confused where it said only one value in step 2 and how it was different from the example problem

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0i actually figured it out why it was wrong and not fitting in i thought i was in the wrong problem but i wasn't if you go all the way back up to step 2 where you typed it STEP 2: multiply 2 to 2x+y+2z=1 > 4x+2y+4z=2 ADD : x2y4z=10 +4x+2y+4z=2 ___________ 5x +0+0=8>(2) the part saying 2x+y+2z=1 was supposed to be 2x+y+2z=10 and then it would simplify to 5x=0 and then x=0 and the eventually get x=0, y=3, and then z=4

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0i basically just redid all the steps you shown me to finish it

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2okk, so the question had 2x+y+2z=10 instead of 2x+y+2z=1

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i think i mistyped up there so well still thanks for your help you helped me understand a lot of it so it should be good :)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2ok, but then i get the solutions as x=2 y=0.5 z=3.25

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0i put 1 instead of 5 in the middle one

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0of the original equations

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so that was a mistake on my part of typing

gdogthegirl
 2 years ago
Best ResponseYou've already chosen the best response.0yeah thank you for helping
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.