x+y=1320;x*y=6

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for example:
2x+y=8
x+3y=14

Solution for x+y=1320;x*y=6 system of equations: 


  • /| x+y-1320 = 0| x*y-6 = 0
  • We try to solve the equation: x+y-1320 = 0
  • x+y-1320 = 0 // - x-1320
  • y = -(x-1320)
  • y = 1320-x
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| x*(1320-x)-6 = 0| y = 1320-x
  • x*(1320-x)-6 = 0
  • 1320*x-x^2-6 = 0
  • 1320*x-x^2-6 = 0
  • DELTA = 1320^2-(-6*(-1)*4)
  • DELTA = 1742376
  • DELTA > 0, so the uquation has 2 solutions
  • x = (1742376^(1/2)-1320)/(-1*2) or x = (-1742376^(1/2)-1320)/(-1*2)
  • x = (2*435594^(1/2)-1320)/(-2) or x = (-2*435594^(1/2)-1320)/(-2)
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = (2*435594^(1/2)-1320)/(-2)
  • For y = 1320-x: 
  • y = 1320-((2*435594^(1/2)-1320)/(-2))
  • y = 1320-((1*2*435594^(1/2)-1320)/(-2))
  • y = 1320-((2*435594^(1/2)-1320)/(-2))
  • We get a system of equations:
  • /| y = 1320-((2*435594^(1/2)-1320)/(-2))| x = (2*435594^(1/2)-1320)/(-2)
  • 2) For x = (-2*435594^(1/2)-1320)/(-2)
  • For y = 1320-x: 
  • y = 1320-((-2*435594^(1/2)-1320)/(-2))
  • y = 1320-((-2*1*435594^(1/2)-1320)/(-2))
  • y = 1320-((-2*435594^(1/2)-1320)/(-2))
  • We get a system of equations:
  • /| y = 1320-((-2*435594^(1/2)-1320)/(-2))| x = (-2*435594^(1/2)-1320)/(-2)

 

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