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anonymous

  • one year ago

**GOLD MEDAL WILL BE GIVEN TO WHO HELPS :) ** Choose the equivalent system of linear equations that will produce the same solution as the one given below. 4x - y = -11 2x + 3y = 5 A) -4x - 9y = -19 -10y = -30 B) 4x + 3y = 5 2y = -6 C) 7x - 3y = -11 9x = -6 D) 12x - 3y = -33 14x = -28

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  1. anonymous
    • one year ago
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    @manutd30

  2. DanJS
    • one year ago
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    multiply the first equation by 3 , then add them together...

  3. DanJS
    • one year ago
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    The basic rules are, you can multiply an equation by a constant value rearrange equations and add equations together...

  4. anonymous
    • one year ago
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    @DanJS what do you mean multiply them?

  5. DanJS
    • one year ago
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    If you multiply an entire equation by a constant number, the equation is unchanged... \[3*[4x-y=-11]\]

  6. DanJS
    • one year ago
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    So when you do that then add the two together, a variable goes to zero and drops out

  7. DanJS
    • one year ago
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    The result after multiplying the first by 3 is there, and now add the two together... 12x - 3y = -33 2x + 3y = 5 ------------------

  8. DanJS
    • one year ago
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    14x = -29

  9. DanJS
    • one year ago
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    you want to find a number you can multiply each equation by, so that when added together, you have a variable drop out. In this case -3y + 3y = 0y

  10. anonymous
    • one year ago
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    @DanJS so I would have to do this to each one ?

  11. DanJS
    • one year ago
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    Here i will do each basic step for this example.....

  12. DanJS
    • one year ago
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    4x - 1y = -11 2x + 3y = 5 If added together, you just will get 6x + 2y = -6

  13. DanJS
    • one year ago
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    you see that so far?

  14. anonymous
    • one year ago
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    yes I see @DanJS

  15. DanJS
    • one year ago
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    ok, so think of some number you can multiply one of the equations by , so that when added will result in zero for one variable...

  16. DanJS
    • one year ago
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    if you multiply the first by 3, you will have a -3y in the first and a +3y in the second

  17. DanJS
    • one year ago
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    you see what i mean ?

  18. DanJS
    • one year ago
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    3*[4x - y = -11] 1*[2x + 3y = 5] ------------------- that is the same as the original, you can multiply both sides of the equation by a number

  19. anonymous
    • one year ago
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    @DanJS yes I see! so it would leave me with Answer B correct??

  20. DanJS
    • one year ago
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    no, lets continue....

  21. DanJS
    • one year ago
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    If you carry out what is above.. you get 12x - 3y = -11 2x + 3y = 5 ---------------- That was the point, now when added the y term goes to zero

  22. DanJS
    • one year ago
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    sorry 12x - 3y = -33 2x + 3y = 5 ------------------

  23. DanJS
    • one year ago
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    now add them together, both sides of the equals

  24. anonymous
    • one year ago
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    14x=28!

  25. DanJS
    • one year ago
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    right !, remember those two basic rules... and the goal of getting a variable to go to zero like the Y did here

  26. DanJS
    • one year ago
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    Multiplying an equation by a constant number, and Adding two equations together... that is it

  27. anonymous
    • one year ago
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    @DanJS this really helped, thank you for explaining this to me!

  28. DanJS
    • one year ago
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    I could type all the dumb script rules in, but those are the ideas

  29. DanJS
    • one year ago
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    One step further.....

  30. DanJS
    • one year ago
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    Say you have one that has terms on the Y like this ... 3y = 10 ... 2y = 41

  31. DanJS
    • one year ago
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    How to get those to add and cancel out... multiply the first by +2 Multiply the second by -3

  32. DanJS
    • one year ago
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    6y -6y ----- 0y

  33. DanJS
    • one year ago
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    just take care of the X and right side of the = when you multiply through and add too

  34. DanJS
    • one year ago
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    That is it... good luck

  35. anonymous
    • one year ago
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    @DanJS wow you make this very easy, definitely writing these in my notes! thank you so much!

  36. DanJS
    • one year ago
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    welcome, practice.. hehe

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