(x*x)+(y*y)=5;6x+5y=-4

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Solution for (x*x)+(y*y)=5;6x+5y=-4 system of equations: 


  • /| x*x+y*y-5 = 0| 6*x+5*y+4 = 0
  • We try to solve the equation: 6*x+5*y+4 = 0
  • 6*x+5*y+4 = 0 // - 6*x+4
  • 5*y = -(6*x+4) // : 5
  • y = (-(6*x+4))/5
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| ((-(6*x+4))/5)*((-(6*x+4))/5)+x*x-5 = 0| y = (-(6*x+4))/5
  • ((-6*x-4)^2)/(5^2)+x^2-5 = 0
  • 61/25*x^2+48/25*x-5+16/25 = 0
  • 61/25*x^2+48/25*x-109/25 = 0
  • 61/25*x^2+48/25*x-109/25 = 0
  • DELTA = (48/25)^2-(-109/25*61/25*4)
  • DELTA = 1156/25
  • DELTA > 0, so the uquation has 2 solutions
  • x = ((1156/25)^(1/2)-48/25)/(2*61/25) or x = (-(1156/25)^(1/2)-48/25)/(2*61/25)
  • x = 1 or x = -109/61
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = -109/61
  • For y = (-(6*x+4))/5: 
  • y = (-(4-109/61*6))/5
  • y = (-(4-654/61))/5
  • y = 410/61/5
  • y = 82/61
  • We get a system of equations:
  • /| y = 82/61| x = -109/61
  • 2) For x = 1
  • For y = (-(6*x+4))/5: 
  • y = (-(1*6+4))/5
  • y = (-(4+6))/5
  • y = -10/5
  • y = -2
  • We get a system of equations:
  • /| y = -2| x = 1

 

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