x/2-y/3=5/6;x/5-y/4=57/10

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

Solution for x/2-y/3=5/6;x/5-y/4=57/10 system of equations: 


  • /| x/2-(y/3)-(5/6) = 0| x/5-(y/4)-(57/10) = 0
  • We try to solve the equation: x/2-(y/3)-(5/6) = 0
  • 1/2*x-1/3*y-5/6 = 0 // - 1/2*x-5/6
  • -1/3*y = -(1/2*x-5/6) // : -1/3
  • y = (-(1/2*x-5/6))/(-1/3)
  • y = -3*(5/6-(1/2*x))
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| x/5-((-3*(5/6-(1/2*x)))/4)-(57/10) = 0| y = -3*(5/6-(1/2*x))
  • (-3*(-1)*(5/6-1/2*x))/4+x/5-57/10 = 0
  • 5/8-7/40*x-57/10 = 0
  • -7/40*x-203/40 = 0
  • -7/40*x-203/40 = 0 // + 203/40
  • -7/40*x = 203/40 // : -7/40
  • x = 203/40/(-7/40)
  • x = -29
  • We insert the solution into one of the initial equations of our system of equations
  • For y = -3*(5/6-(1/2*x)): 
  • y = -3*(5/6-(-29*1/2))
  • y = -3*(5/6+29/2)
  • y = -3*46/3
  • y = -46
  • We get a system of equations:
  • /| y = -46| x = -29

 

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