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iiamentertainment

  • one year ago

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

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  1. iiamentertainment
    • one year ago
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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 ?

  2. iiamentertainment
    • one year ago
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    @CalebBeavers

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

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

  5. iiamentertainment
    • one year ago
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    Algebra 2

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

  7. iiamentertainment
    • one year ago
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    im familar with substitution

  8. abb0t
    • one year ago
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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?

  9. abb0t
    • one year ago
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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.

  10. iiamentertainment
    • one year ago
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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

  11. abb0t
    • one year ago
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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.

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

  13. abb0t
    • one year ago
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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.

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

  15. abb0t
    • one year ago
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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!

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

  17. LogicalApple
    • one year ago
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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

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

  19. LogicalApple
    • one year ago
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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 ?

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

  21. iiamentertainment
    • one year ago
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    @LogicalApple

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

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

  24. LogicalApple
    • one year ago
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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

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

  26. LogicalApple
    • one year ago
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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.

  27. LogicalApple
    • one year ago
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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

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

  29. LogicalApple
    • one year ago
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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

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

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

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

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

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

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

  36. iiamentertainment
    • one year ago
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    @LogicalApple

  37. LogicalApple
    • one year ago
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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.

  38. iiamentertainment
    • one year ago
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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

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

  40. abb0t
    • one year ago
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    Correct :)

  41. biasophia
    • 8 months ago
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    solve the system of equations by elimination 3x+y+2z=3 2x-3y-z=3 x+2y+z=4

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