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gdogthegirl

Ok i have to solve this equation by using elimination and the steps are

  • one year ago
  • one year ago

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  1. gdogthegirl
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    Step 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 x-2y-4z=-10 2x+y+2z=1 3x-3y-2z=1 Step 1: (2x+y+2z=5) +(3x-3y-2z=1) which then equals 5x+y=6 simplified Step 2: x-2y-4z=-10 2(2x+y+2z=5) (x-2y-4z=-10) +(4x+2y+4z=10) and then i got stuck because now there is two opposite coefficients

    • one year ago
  2. hartnn
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    in STEP 1, what is y-3y ??

    • one year ago
  3. hartnn
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    its not y

    • one year ago
  4. gdogthegirl
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    oh i ment to type -2y i had a mess of my notes/work

    • one year ago
  5. hartnn
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    ok,so u get 5x-2y=6

    • one year ago
  6. gdogthegirl
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    okay than what next

    • one year ago
  7. hartnn
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    now ADD (x-2y-4z=-10) +(4x+2y+4z=10) what u get ?

    • one year ago
  8. hartnn
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    oh wait, how did u get 10 ?

    • one year ago
  9. hartnn
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    it shouls be 2, isn't it ?

    • one year ago
  10. hartnn
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    (x-2y-4z=-10) +(4x+2y+4z=2)

    • one year ago
  11. gdogthegirl
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    you have to make another set of coefficients by modifying the problem so i times 2 by the equation 2x+y+2z=5

    • one year ago
  12. gdogthegirl
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    and i tryed not timeing it by two but the variables missing have to be the same in both equations

    • one year ago
  13. hartnn
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    wait, where did u get 5 from ? isn't that 1 in original question ?

    • one year ago
  14. gdogthegirl
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    yes 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

    • one year ago
  15. hartnn
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    wait, i will write first 2 steps , u check

    • one year ago
  16. gdogthegirl
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    here 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.

    • one year ago
  17. gdogthegirl
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    it is super confusing to me

    • one year ago
  18. hartnn
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    i will write step 1 and 2 ,see whether it make sense.

    • one year ago
  19. gdogthegirl
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    oh ok

    • one year ago
  20. hartnn
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    STEP 1: ADD 2x+y+2z=1 +3x-3y-2z=1 __________ 5x -2y +0 =2 so 5x-2y=2 ------->(1) STEP 2: multiply 2 to 2x+y+2z=1 ---> 4x+2y+4z=2 ADD : x-2y-4z=-10 +4x+2y+4z=2 ___________ 5x +0+0=-8------>(2) GOT THESE STEPS ?

    • one year ago
  21. gdogthegirl
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    yes

    • one year ago
  22. hartnn
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    now from (2) u directly have 5x=-8 so x= -(8/5) ok ?

    • one year ago
  23. gdogthegirl
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    alright

    • one year ago
  24. hartnn
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    now since u have x, from (1) can u find y ??

    • one year ago
  25. gdogthegirl
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    not 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

    • one year ago
  26. hartnn
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    no! in (1) u only have x and y and u got value of x..... 5x-2y=2 put x= -8/5 here ------^

    • one year ago
  27. gdogthegirl
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    oh ok so 5(-8/5)-2y=2 and y = -5

    • one year ago
  28. gdogthegirl
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    and then you would substitute those into one of the original equations right?

    • one year ago
  29. hartnn
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    thats right! y=-5 :) yes, now u have x and y substitute in any of the original equation, u will get z ...

    • one year ago
  30. gdogthegirl
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    (-8/5)-2(-5)-4z=-10 i get x=22/5 is that right????

    • one year ago
  31. gdogthegirl
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    i 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

    • one year ago
  32. hartnn
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    z is actually, 23/5=4.6 x= -8/5=-1.6 try putting -1.6,-5,4.6

    • one year ago
  33. gdogthegirl
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    i was on the wrong practice problem duh sorry my brain got all confused with all this thank you so much for all your help :)))))

    • one year ago
  34. hartnn
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    lol! its ok. but did u understand the process ?

    • one year ago
  35. gdogthegirl
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    yeha i mainly got confused where it said only one value in step 2 and how it was different from the example problem

    • one year ago
  36. gdogthegirl
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    i 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 : x-2y-4z=-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

    • one year ago
  37. gdogthegirl
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    my bad z=4

    • one year ago
  38. gdogthegirl
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    i basically just redid all the steps you shown me to finish it

    • one year ago
  39. hartnn
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    okk, so the question had 2x+y+2z=10 instead of 2x+y+2z=1

    • one year ago
  40. gdogthegirl
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    yeah 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 :)

    • one year ago
  41. hartnn
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    ok, but then i get the solutions as x=2 y=-0.5 z=3.25

    • one year ago
  42. gdogthegirl
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    i put 1 instead of 5 in the middle one

    • one year ago
  43. gdogthegirl
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    of the original equations

    • one year ago
  44. gdogthegirl
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    so that was a mistake on my part of typing

    • one year ago
  45. hartnn
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    x=0 y=-3 z=4

    • one year ago
  46. hartnn
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    yup, u are correct then

    • one year ago
  47. gdogthegirl
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    yeah thank you for helping

    • one year ago
  48. hartnn
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    welcome :)

    • one year ago
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