SOLUTION: When each of three numbers is added to twice the sum of the other two, the results are 64, 62 and 59. Determine the numbers (algebraically). I have come up with the equations:

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Question 997872: When each of three numbers is added to twice the sum of the other two, the results are 64, 62 and 59. Determine the numbers (algebraically).
I have come up with the equations:
a+2(b+c)=64
b+2(a+c)=62
c+2(b+a)=59
I am unsure of how to further solve for the unknown values.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!







    1    2    2      64
    2    1    2      62
    2    2    1      59

-2R1 + R2 -> R2
-2R1 + R3 -> R3

    1    2    2      64
    0   -3   -2     -66
    0   -2   -3     -69

-1/3R2 -> R2

    1    2    2      64
    0    1    2/3    22
    0   -2   -3     -69

2R2 + R3 -> R3

    1    2    2      64
    0    1    2/3    22
    0    0   -5/3   -25  

-3/5R3 -> R3

    1    2    2      64
    0    1    2/3    22
    0    0    1      15

-2/3R3 + R2 -> R2

    1    2    2      64
    0    1    0      12
    0    0    1      15

-2R2 - 2R3 + R1 -> R1

    1    0    0      10
    0    1    0      12
    0    0    1      15


John

My calculator said it, I believe it, that settles it

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