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need_help!

  • 2 years ago

Find an ordered pair that is a solution of the system 4 2 1 3 2 3 x y x y + = - - =

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  1. need_help!
    • 2 years ago
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    What the..? Wait.

  2. need_help!
    • 2 years ago
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    4x+2y=-1 3x-2y=3

  3. Hero
    • 2 years ago
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    Add the equations together and what do you get?

  4. need_help!
    • 2 years ago
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    Hmm

  5. need_help!
    • 2 years ago
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    How do I add them?

  6. chris
    • 2 years ago
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    Combine all of the like terms. Since you know that 4x+2y=-1 and 3x-2y=3, you also know that 4x+2y + 3x -2y = -1 + 3

  7. need_help!
    • 2 years ago
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    so, x=2/7 ?

  8. chris
    • 2 years ago
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    good work =)

  9. chris
    • 2 years ago
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    now how do you get y when x=2/7?

  10. need_help!
    • 2 years ago
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    umm, i think you just substitute right? O.o

  11. chris
    • 2 years ago
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    yep =) [just plug x=2/7 back into either equation]

  12. need_help!
    • 2 years ago
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    Yay! This is easy =D Thank youu.

  13. chris
    • 2 years ago
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    No problem. Now the general way to solve these types of problems (systems of equations), is to solve for one variable first, and then substitute back into the other equation. To do this, you mus have a separate equation for each unknown variable - for example in this problem there are two equations and two unknowns.

  14. need_help!
    • 2 years ago
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    Yes I get it! But for example you have like: 4x+4y=-1 3x-2y=3 What do you do here? you can't cancel the 'y' or 'x' out

  15. chris
    • 2 years ago
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    well, you actually can if you know a small trick.

  16. chris
    • 2 years ago
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    if you know that 3x - 2y = 3, you can multiply both sides by the same number and the equation will still be true (equivalent)

  17. chris
    • 2 years ago
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    in this case, I can multiply both sides by 2

  18. chris
    • 2 years ago
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    so 2(3x -2y) = 2*3

  19. chris
    • 2 years ago
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    6x - 4y = 6

  20. chris
    • 2 years ago
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    Now you can cancel out all of the y's by adding the two equations

  21. chris
    • 2 years ago
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    4x + 4y = 4 6x - 4y = 6

  22. need_help!
    • 2 years ago
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    Aooh! *smart* :P :D

  23. need_help!
    • 2 years ago
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    I like it! Thanks a lot for the help.

  24. chris
    • 2 years ago
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    No problem. There are other ways to solve these types of problems, but just ask here when you find a case where it's hard to find a way to cancel out =). good luck!

  25. need_help!
    • 2 years ago
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    btw, the ordered pairs are : (0,-5/14) and (2/7,0) ?

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