algebraic systems

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ok, so im stumped on this bonus system. there is a hint that the prof. gave that said that all coefficients are 1 or -1. can someone do this and explain how you did it?

a + b + c + d + e + f + g + h + k + m = 27
a – b + c + d + e + f + g + h + k + m = 23
a + b - c + d + e + f + g + h +k +m = 39
a + b + c - d + e + f + g + h + k + m = -3
a + b + c + d - e + f + g + h + k + m = 21
a + b + c + d + e - f + g + h + k + m = -13
a + b + c + d + e + f - g + h + k + m = -5
a + b + c + d + e + f + g - h + k - m = 11
a + b + c + d + e + f + g + h - k + m = -9
a + b + c + d + e + f + g + h + k - m = 1

  • algebraic systems -

    a+b+c+d+e+f+g+h+k+m = 27
    a–b+c+d+e+f+g+h+k+m = 23

    subtract the equations to get
    2b = 4, so
    b=2

    work with other pairs of equations to evaluate the other variables. Look for a pair which are identical except for the ± sign on one variable.

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