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  1. #1
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    equations

    Solve the following system of simultaneous equations:
    6x1 + 4x2 = 40
    2x1 + 3x2 = 20

    I'm a little confused, can one help.
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  2. #2
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    Quote Originally Posted by sweettea331
    Solve the following system of simultaneous equations:
    6x1 + 4x2 = 40
    2x1 + 3x2 = 20

    I'm a little confused, can one help.
    I'm a Physicist, so I usually don't do the fancier methods...

    Substitution method. Solve one equation for one of the unknowns, then plug it into the other equation. I'll solve the top equation first:
    6x_1+4x_2=40
    Thus x_2=1/4*(40-6x_1)=10-3/2*x_1

    Now use this value for x_2 in the second equation. This leaves us an equation in 1 unknown ( x_1).
    2x_1+3(10-3/2*x_1)=20
    2x_1+30-9/2*x_1=20
    -5/2*x_1+30=20

    So, solve this equation for x_1. Use this value in either of the original equations to get a value for x_2. (I get x_1=4 and x_2=4).

    There are other methods to use. One of them is to multiply the first equation by a constant and the second by another constant such that you can subtract the two equations and cancel out one of the variables. In this case, you don't need to do anything to the first equation. Multiply the second equation by 3:
    6x_1+4x_2=40
    6x_1+9x_2=60

    Now we subtract the two equations from each other:
    6x_1+4x_2=40
    -6x_1-9x_2=-60
    ----------------------------------
    0-5x_2=-20
    This gives a value for x_2. Then use this x_2 in either of the original equations and solve for x_1.

    -Dan
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