x+y=1;x^5+y^5=31

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2x+y=8
x+3y=14

Solution for x+y=1;x^5+y^5=31 system of equations: 


  • /| x+y-1 = 0| x^5+y^5-31 = 0
  • We try to solve the equation: x+y-1 = 0
  • x+y-1 = 0 // - x-1
  • y = -(x-1)
  • y = 1-x
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| (1-x)^5+x^5-31 = 0| y = 1-x
  • (1-x)^5+x^5-31 = 0
  • 5*x^4-10*x^3+10*x^2-5*x-31+1 = 0
  • 5*x^4-10*x^3+10*x^2-5*x-30 = 0
  • 5*x^4-10*x^3+10*x^2-5*x-30 = 0
  • 5*(x^4-2*x^3+2*x^2-x-6) = 0
  • x^4-2*x^3+2*x^2-x-6 = 0
  • Potencjalne pierwiastki cau0142kowite to: { 1, -1, 2, -2, 3, -3, 6, -6 }
  • Sprawdzamy: 1
  • For x = 1, mamy: x^4-2*x^3+2*x^2-x-6 = -6
  • 1 nie jest pierwiastkiem
  • Sprawdzamy: -1
  • For x = -1, mamy: x^4-2*x^3+2*x^2-x-6 = 0
  • -1 jest pierwiastkiem
  • Mou017Cemy zredukowau0107 stopieu0144 wielomianu poby podzielenie go by: x+1
  • x^3-3*x^2+5*x-6
  • x^4-2*x^3+2*x^2-x-6:x+1
  • -x^4-x^3
  •  2*x^2-3*x^3-x-6
  •  3*x^3+3*x^2
  •  5*x^2-x-6
  •  -5*x^2-5*x
  •  -6*x-6
  •  6*x+6
  •  0
  • x^3-3*x^2+5*x-6 = 0
  • Potencjalne pierwiastki cau0142kowite to: { 1, -1, 2, -2, 3, -3, 6, -6 }
  • Sprawdzamy: 1
  • For x = 1, mamy: x^3-3*x^2+5*x-6 = -3
  • 1 nie jest pierwiastkiem
  • Sprawdzamy: -1
  • For x = -1, mamy: x^3-3*x^2+5*x-6 = -15
  • -1 nie jest pierwiastkiem
  • Sprawdzamy: 2
  • For x = 2, mamy: x^3-3*x^2+5*x-6 = 0
  • 2 jest pierwiastkiem
  • Mou017Cemy zredukowau0107 stopieu0144 wielomianu poby podzielenie go by: x-2
  • x^2-x+3
  • x^3-3*x^2+5*x-6:x-2
  • 2*x^2-x^3
  •  5*x-x^2-6
  •  x^2-2*x
  •  3*x-6
  •  6-3*x
  •  0
  • x^2-x+3 = 0
  • DELTA = (-1)^2-(1*3*4)
  • DELTA = -11
  • DELTA < 0, wiu0119c ru00F3wnanie nie ma rozwiu0105zau0144
  • x in { -1, 2} 
  • 5 = 0
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = -1
  • For y = 1-x: 
  • y = 1+1
  • y = 2
  • We get a system of equations:
  • /| y = 2| x = -1
  • 2) For x = 2
  • For y = 1-x: 
  • y = 1-2
  • y = -1
  • We get a system of equations:
  • /| y = -1| x = 2

 

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