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iiamentertainment Group Title

What is the solution of the system of equations? { 2x + 2y + 3z = -6 3x + 5y + 4z = 3 2x + 3y + 4z = - 10} Three equations

  • one year ago
  • one year ago

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  1. iiamentertainment Group Title
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    So 2x + 2y + 3z = -6 2y + 3z = -2x - 6 2y = -2x -3z - 6 y = -2x -3z - 6/2 y = -x -3/2z - 3 ?

    • one year ago
  2. iiamentertainment Group Title
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    @CalebBeavers

    • one year ago
  3. iiamentertainment Group Title
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    @abb0t please help ..

    • one year ago
  4. abb0t Group Title
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    What class is this for?

    • one year ago
  5. iiamentertainment Group Title
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    Algebra 2

    • one year ago
  6. abb0t Group Title
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    Well, you can use 1 of 2 methods. Substitution, or Elimination. Are you familiar with either of them?

    • one year ago
  7. iiamentertainment Group Title
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    im familar with substitution

    • one year ago
  8. abb0t Group Title
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    Ah, I almost want to suggest using gauss-elimination, but that's beyond algebra 2. Well, I think it might be easier to use elimination actually to eliminate one equation first and then a second to get 2-variable equations. Does that make sense?

    • one year ago
  9. abb0t Group Title
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    Hint, start by eliminating the x's since equations (1) and (3) both begin with 2. Multiply the first (or second) by -1.

    • one year ago
  10. iiamentertainment Group Title
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    Um im not that good with elimination , butf you walk me through and let me solve it i think ill be ok

    • one year ago
  11. abb0t Group Title
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    Yes. I will walk you through it, mate. Start by eliminating one variable in the system of equations. As I said before, It might be easier to eliminate the x from equations (1) and (3) since they both begin with the number 2 [NOTE: Do NOT do anything to eq (2), yet]. You can do this by multiplying either (1) or (3) by -1. Try it and let me know which one you choose and what ur answer is.

    • one year ago
  12. iiamentertainment Group Title
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    -1(2x + 2y + 3z)= -6 -2x - 2y - 3z = -6 ?

    • one year ago
  13. abb0t Group Title
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    You're 90% correct, when you multiply (-1) to the eq, you also have to multiply it to the -6 and you know (-1)(-6) = 6. making eq(1) -2x-2y-3z = 6 I'm going to use the term: eq(#) just so I type less :P But notice that eq(1) and eq(2) can be added. And the x' term cancels out nicely. So that you get a new equation with only y's and z's. When you add everything! Including the 6 and -10. Try it.

    • one year ago
  14. iiamentertainment Group Title
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    2x + 3y + 4z = - 10 -2x - 2y - 3z = 6 y + 1 = -4 y = -5 ?

    • one year ago
  15. abb0t Group Title
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    i have to step out for a moment, but I will tell you the next few steps. Next, do the same thing to eliminate x! from eq(2)! To get a second equation with only y's and z's! Notice that now you have TWO system of equations which you can use elimination (again) or substitution (which you said you like) to solve for either y or z! Once you have your y or z value, plug it back into the original 2 system equation to solve for either y or z (which ever variable you chose to solve for). Once you solved for the 2nd variable you should have TWO variables: y AND z! Now plug in everything into ANY of the equations of the 3-systems and solve for x! You can check by plugging everything in and you should get either -6, 3, or -10! If you are correct, you should get those answers!

    • one year ago
  16. iiamentertainment Group Title
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    @blondie16 can you help , im confused

    • one year ago
  17. LogicalApple Group Title
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    You are certainly on the right track. You seem to have forgotten the 'z' variable when adding "4z" and "-3z". This gives you a z. So your equation becomes: y + z = -4

    • one year ago
  18. iiamentertainment Group Title
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    Ok thats what i did wrong ok cool, then what

    • one year ago
  19. LogicalApple Group Title
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    What @abb0t suggested next was to use elimination once more. This time with eq(1) and eq(2). The focus here is to, again, eliminate the 'x' variable. equation 1: 2x + 2y + 3z = -6 equation 2: 3x + 5y + 4z = 3 If you multiply eq(1) by -3/2 you will be able to then add it to eq(2) to cancel out the 'x' again. What do you obtain when you multiply eq(1) through by -3/2 ?

    • one year ago
  20. iiamentertainment Group Title
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    -3/2(2x + 2y + 3z) = -6 -3x - 3y - 4.5z = 9 3x + 5y + 4z = 3 2y -.5z = 6 ?

    • one year ago
  21. iiamentertainment Group Title
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    @LogicalApple

    • one year ago
  22. LogicalApple Group Title
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    The 9 + 3 should be a 12 so 2y - 0.5z = 12

    • one year ago
  23. iiamentertainment Group Title
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    i thoue were subtractingnot adding

    • one year ago
  24. LogicalApple Group Title
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    -3x + 3x = 0 -3y + 5y = 2y -4.5z + 4z = -0.5z 9 + 3 = 12 You added everything else correctly but the last numbers

    • one year ago
  25. iiamentertainment Group Title
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    Oh Ok , Next Step?

    • one year ago
  26. LogicalApple Group Title
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    In any event you are now down to a system of 2 equations with 2 variables y + z = -4 2y - 0.5z = 12 You can use substitution at this point.

    • one year ago
  27. LogicalApple Group Title
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    Notice how the elimination method eliminates one of the variables, leaving you with only two to deal with. From here you could set y = -4 - z in the first equation and substitute this value of y into the second equation and solve for z

    • one year ago
  28. iiamentertainment Group Title
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    2x + 2(-4 -z) + 3z = -6 like that

    • one year ago
  29. LogicalApple Group Title
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    No, I meant the second equation listed here: y + z = -4 2y - 0.5z = 12 Not any of the original equations

    • one year ago
  30. iiamentertainment Group Title
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    2(-4 -z) - 0.5z = 12 -8 - 2z - .5z = 12 -8 + 3z = 12 3z = 20 z = 6.67

    • one year ago
  31. LogicalApple Group Title
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    -2z - 0.5z = -2.5z So you should have -8 - 2.5z = 12

    • one year ago
  32. iiamentertainment Group Title
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    -8 - 2.5z = 12 -2.5z = 20 z = -8

    • one year ago
  33. LogicalApple Group Title
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    Yes, that's it!

    • one year ago
  34. LogicalApple Group Title
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    And we know: y + z = -4

    • one year ago
  35. iiamentertainment Group Title
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    y + (-8) = -4 y = 4

    • one year ago
  36. iiamentertainment Group Title
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    @LogicalApple

    • one year ago
  37. LogicalApple Group Title
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    Yes, that is also correct. Now you know what y and z are. Use these values in any one of the original three equations and you will obtain the value for x.

    • one year ago
  38. iiamentertainment Group Title
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    2x + 2(4) + 3(-8) = -6 2x + 8 - 24 = -6 2x - 16 = -6 2x = 10 x = 5 y = 4 z = -8 @LogicalApple

    • one year ago
  39. LogicalApple Group Title
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    Fantastic. (5, 4, -8) is the correct solution

    • one year ago
  40. abb0t Group Title
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    Correct :)

    • one year ago
  41. biasophia Group Title
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    solve the system of equations by elimination 3x+y+2z=3 2x-3y-z=3 x+2y+z=4

    • 4 months ago
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