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At the end of a problem I'm solving, I have a series of equations including 4 variables. It is as follows:

x = y/4 + z/7 + m/7

y = 6x/13 + 2z/7 + 3m/7

z = 3x/13 + y/4 + 3m/7

m = 4x/13 + y/2 + 4z/7

x + y + z + m =1

I should find the value of x. What method should I follow? I've been trying so hard on it for a while and I'm clueless now :(

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  • $\begingroup$ "I've been trying so hard": what did you try, precisely ? $\endgroup$
    – user997569
    Nov 30 '21 at 15:52
  • $\begingroup$ Tried to do Gaussian and variable elimination. $\endgroup$
    – Ceren
    Nov 30 '21 at 15:57
  • $\begingroup$ And what went wrong ? $\endgroup$
    – user997569
    Nov 30 '21 at 15:58
  • $\begingroup$ I just could not find the right answer, then I doubted using Gaussian. Now I see that I'm just bad at artihmetics. $\endgroup$
    – Ceren
    Nov 30 '21 at 16:02
  • $\begingroup$ I confirm that the coefficients do not simplify nicely. $\endgroup$
    – user997569
    Nov 30 '21 at 16:03
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If you just want the answer, wolframalpha.com can help (https://www.wolframalpha.com/input/?i=x+%3D+y%2F4+%2B+z%2F7+%2B+m%2F7%2C+y+%3D+6x%2F13+%2B+2z%2F7+%2B+3m%2F7%2C+z+%3D+3x%2F13+%2B+y%2F4+%2B+3m%2F7%2C+m+%3D+4x%2F13+%2B+y%2F2+%2B+4z%2F7%2C+x+%2B+y+%2B+z+%2B+m+%3D1), which would give you x=13/86.

But in general, such a system of linear equations is solved through gaussian elimination (https://en.wikipedia.org/wiki/Gaussian_elimination#Example_of_the_algorithm)

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  • $\begingroup$ Thanks. I tried Gaussian, must have calculated stuff wrong since numbers are complex. $\endgroup$
    – Ceren
    Nov 30 '21 at 15:49
  • $\begingroup$ @Ceren numbers are not complex. $\endgroup$
    – CroCo
    Nov 30 '21 at 19:40
  • $\begingroup$ I know, I meant complicated $\endgroup$
    – Ceren
    Nov 30 '21 at 20:54

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