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Solve the following simultaneous equations:


\displaystyle{\begin{cases}2x_1+x_2+x_3+x_4+x_5 = 6 \\ x_1+2x_2+x_3+x_4+x_5 = 12 \\ x_1+x_2+2x_3+x_4+x_5=24\\ x_1+x_2+x_3+2x_4+x_5=48 \\ x_1+x_2+x_3+x_4+2x_5 = 96\end{cases}}

User Staszek
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1 Answer

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First step, let's call the sum of all unknowns as k.

Then the system becomes:


  • x_1+k=6

  • x_2+k=12

  • x_3+k=24

  • x_4+k=48

  • x_5+k=96

Second step, add up all equations to get:

  • k + 5k = 6 + 12 + 24 + 48 + 96
  • 6k = 186
  • k = 31

Last step, substitute the value of k back into secondary equations and find each unknown:

  • x₁ = - 25
  • x₂ = - 19
  • x₃ = - 7
  • x₄ = 17
  • x₅ = 65

User Sharat Chandra
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