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Math Help - Find X and Y

  1. #1
    Newbie sarah3asal's Avatar
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    Find X and Y

    Hello.. Could someone pleaseee help me find X and Y and show me the steps how you got it?

    300x + 100y = 900
    400x + 200y = 2200
    100x + 200y = 800
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  2. #2
    MHF Contributor
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    Quote Originally Posted by sarah3asal View Post
    Hello.. Could someone pleaseee help me find X and Y and show me the steps how you got it?

    300x + 100y = 900
    400x + 200y = 2200
    100x + 200y = 800
    There are many ways to do this, even without investigating first.
    But I see that there are 3 equations given while there are only two unknowns or variables. We need only two independent equations to solve for two unknowns. The 3rd extraneous equation could mean trouble.

    300x + 100y = 900 ----------(1)
    400x + 200y = 2200 --------(2)
    100x + 200y = 800 -----------(3)

    Since they are all in 100's, let us reduce them all into their simplest forms by dividing them all by 100,
    3x + y = 9 -----------------(1a)
    4x + 2y = 22 --------------(2a)
    x + 2y = 8 ----------------(3a)

    Since there are only two unknowns, we will use only to equations and then let us see if the 3rd equation will accept the solved x and y from the said two equations.
    Let's use (1a) and (2a) only.

    One popular way of doing this is by substitution.
    From (1a), y = 9 -3x
    Substitute that into (2a),
    4x +2(9 -3x) = 22
    4x +18 -6x = 22
    4x -6x = 22 -18
    -2x = 4
    x = 4 / -2
    x = -2 ------------------------------**
    And, y = 9 -3(-2) = 9 +6 = 15 -------**

    Would the Eq.(3a) be satisfied with those?
    x + 2y = 8 ----------------(3a)
    -2 +2(15) =? 8
    -2 +30 =? 8
    28 =? 8
    No!
    Trouble, just as I thought.

    What it means is that the 3 given independent equations do not have a common point they can agree on. :-)
    Meaning, for the 3 given equations, there is no solution.
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