5/x+2/y=16;3/x-5/y=-9

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Solution for 5/x+2/y=16;3/x-5/y=-9 system of equations: 


  • /| 5/x+2/y-16 = 0| 3/x-(5/y)+9 = 0
  • We try to solve the equation: 5/x+2/y-16 = 0
  • 2*y^-1 = -(5*x^-1-16) // : 2
  • y^-1 = (16-(5*x^-1))/2
  • -1 < 0
  • 1/(y^1) = (16-(5*x^-1))/2 // * y^1
  • 1 = y^1*((16-(5*x^-1))/2) // : (16-(5*x^-1))/2
  • 2*(16-5*x^-1)^-1 = y^1
  • y = 2*(16-5*x^-1)^-1
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| 3/x-(5/(2*(16-5*x^-1)^-1))+9 = 0| y = 2*(16-5*x^-1)^-1
  • (-1*5*(16-5*x^-1))/2+3/x+9 = 0
  • 31/2*x^-1-40+9 = 0
  • 31/2*x^-1-31 = 0
  • 31/2*x^-1 = 31 // : 31/2
  • x^-1 = 2
  • -1 < 0
  • 1/(x^1) = 2 // * x^1
  • 1 = 2*x^1 // : 2
  • 1/2 = x^1
  • x = 1/2
  • We insert the solution into one of the initial equations of our system of equations
  • For y = 2*(16-5*x^-1)^-1: 
  • y = (2*(16-5*(1/2)^-1)^-1)^1
  • y = (2*(16-5*2)^-1)^1
  • y = (2*(16-10)^-1)^1
  • y = (2*6^-1)^1
  • y = (2*(1/6))^1
  • y = (1/6*2)^1
  • y = (1/3)^1
  • y = 1/3
  • We get a system of equations:
  • /| y = 1/3| x = 1/2

 

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