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Math Help - Simultaneous Equations

  1. #1
    Member GAdams's Avatar
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    Simultaneous Equations

    2xy + y = 10 (1)
    x + y = 4 (2)

    I got as far as:

    (2) y = 4 - x

    substitute into (1)

    2x(4-x) + (4-x) = 10

    2x(4-x) + (4-x) -10 = 0

    Question: how to know when/ why to make it equal 0?

    Also, I multiply out and get

    8x - 2x^2 + (4 - x)- 10 = 0

    then, 7x - 2x^2 - 6 = 0

    but the answer has 2x^2 - 7x + 6 = 0 at this stage

    Confused.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by GAdams View Post
    2xy + y = 10 (1)
    x + y = 4 (2)

    I got as far as:

    (2) y = 4 - x

    substitute into (1)

    2x(4-x) + (4-x) = 10

    2x(4-x) + (4-x) -10 = 0

    Question: how to know when/ why to make it equal 0?

    Also, I multiply out and get

    8x - 2x^2 + (4 - x)- 10 = 0

    then, 7x - 2x^2 - 6 = 0

    but the answer has 2x^2 - 7x + 6 = 0 at this stage

    Confused.
    If you are asking, in terms of a procedure, when you should rearrange an equation such that one side is equal to 0, it's going to depend on the method.

    In your case, you simply haven't gone far enough. If you can't factor what you have, use the quadratic formula (or completing the square). I'll factor it:
    2x^2 - 7x + 6 = (2x - 3)(x - 2) = 0

    x = 3/2 or x = 2

    So we need y values for each of these points:
    x = 3/2 ==> y = 4 - 3/2 = 5/2
    x = 2 ==> y = 4 - 2 = 2

    So your solutions are:
    (x, y) = (3/2, 5/2)
    (x, y) = (2, 2)

    -Dan
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  3. #3
    Member GAdams's Avatar
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    OK. I don't understand this:

    after substituting you get:

    8x - 2x^2 + 4 - x - 10 = 0

    How do we end up with

    2x^2 - 7x + 6 = 0

    shouldn't it be:

    7x -2x^2 -6 = 0 ???
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by GAdams View Post
    OK. I don't understand this:

    after substituting you get:

    8x - 2x^2 + 4 - x - 10 = 0

    How do we end up with

    2x^2 - 7x + 6 = 0

    shouldn't it be:

    7x -2x^2 -6 = 0 ???
    Step by step then.

    7x - 2x^2 - 6 = 0

    Multiply both sides by -1:

    (-1)*(7x - 2x^2 - 6) = (-1)*0

    -7x + 2x^2 + 6 = 0

    2x^2 - 7x + 6 = 0

    -Dan
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