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Math Help - Setting two equations equal and simplifying

  1. #1
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    Setting two equations equal and simplifying

    I have 4 equations:

    #1) Q1 = 8900 - P1 + 2P2
    #2) Q1 = 3P1 -1200
    #3) Q2 = 11,000 + 2P1 – 5P2
    #4) Q2 = 14P2 - 150

    I need to set equations #1 and #2 equal to each other and simplify as much as possible.

    I need to do the same thing with equations #3 and #4

    So,

    8900 - P1 + 2P2 = 3P1 -1200

    And,

    11,000 + 2P1 – 5P2 = 14P2 - 150

    I need to simplify each of these as much as possible. Can anyone help?? Please??
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  2. #2
    Junior Member star_tenshi's Avatar
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    Quote Originally Posted by JimmyZ11381 View Post
    I have 4 equations:

    #1) Q1 = 8900 - P1 + 2P2
    #2) Q1 = 3P1 -1200
    #3) Q2 = 11,000 + 2P1 – 5P2
    #4) Q2 = 14P2 - 150

    I need to set equations #1 and #2 equal to each other and simplify as much as possible.

    I need to do the same thing with equations #3 and #4

    So,

    8900 - P1 + 2P2 = 3P1 -1200

    And,

    11,000 + 2P1 – 5P2 = 14P2 - 150

    I need to simplify each of these as much as possible. Can anyone help?? Please??
    Assuming that P1 and P2 are the same for #1-#4, we can simplify and solve this system of equations:
    For simplification, I've replaced P1 = a & P2 = b.
    First: #1 = #2
    \Rightarrow 8900 - a + 2b = 3a - 1200
    \Rightarrow 8900 + 1200 = 3a +a - 2b
    \Rightarrow 10100 = 4a - 2b we can divide by 2 to get:
    \Rightarrow 5050 = 2a - b which we will denote equation (1)

    Second: #3 = #4
    \Rightarrow 11000 + 2a - 5b = 14b - 150
    \Rightarrow 11000 + 150 = -2a + 14b + 5b
    \Rightarrow 10850 = -2a + 19b which we will denote equation (2)

    Then we attempt to solve this linear system of equations by adding the two equations:
    (1) 5050 = 2a - b
    (2) \underline{10850 = -2a + 19b}
    15900 = 18b
    \Rightarrow b = 883\frac{1}{3} = P2

    Then we can substitute this answer back into equation (1):
    (1) 5050 = 2a - b
    \Rightarrow a = \frac{5050+b}{2} = 2966\frac{2}{3} = P1
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