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Math Help - Simultaneous Equations

  1. #1
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    Simultaneous Equations

    How would I do...

    4p-3q=6
    3p-2q=5


    2x=3y-2
    3y=1+4x

    and

    4c + 3t =515
    3c + 5t = 565

    Thanks a lot. Still havent got my head around Simultaneous Equations
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  2. #2
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    Quote Originally Posted by Yppolitia View Post
    2x=3y-2
    3y=1+4x
    You have equation: 3y=1+4x

    Subtract 2x from both sides: 3y-2x=1+4x-2x

    But look at your first equation, you know that 2x equals 3y-2. So substitute: 3y-(3y-2)=1+4x-2x

    Simplify: 3y-3y+2=1+2x

    Therefore: 2=1+2x

    Subtract 1 from both sides: 1=2x

    divide by 2: \frac{1}{2}=x

    Go back to original equation: 2x=3y-2

    Substitute: 2\left(\frac{1}{2}\right)=3y-2

    Multiply: 1=3y-2

    Add 2 to both sides: 3=3y

    Divide by 3: 1=y

    Can you do the other ones?
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  3. #3
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    Quote Originally Posted by Yppolitia View Post
    Thanks a lot. Still havent got my head around Simultaneous Equations
    What is the value of 2+x when x=1? That is all that "Simultaneous" (should be "System of") equations are.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Yppolitia View Post
    How would I do...

    4p-3q=6
    3p-2q=5
    You want to modify the equations so that one of the variables has the same
    coefficient in both the equations, then by subtracting the equations you
    can eliminate that variable.

    In this case if we multiply the first equation by 3 and the second by 4 the
    coefficient of p will be 12 in both cases:

    12p - 9q = 18
    12p - 8q = 20.

    Subtracting these equations gives:

    (12p - 9q) - (12p - 8q) = 18-20,

    or:

    -q = -2,

    so q=2.

    Now we substitute this value of q back into any of the equations that
    we have to find the value of p. So lets take the equation

    4p - 3q = 6,

    with q=2 this becomes:

    4p - 6 = 6,

    or:

    4p = 12,

    so p=3.

    If you reorganise your equations into the standard form with all the unknowns on one side
    (and in the same order in all the equations) and the constants on the other side like the
    above equations, then this method will work for all your problems.

    It has another advantage, in that it can be used with a few more tricks for equations in
    more than two variables (of course with the same number of equations as variables).

    RonL
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