1/3x+1/5y=2/5;1/3x+3y=44/3

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

Solution for 1/3x+1/5y=2/5;1/3x+3y=44/3 system of equations: 


  • /| (1/3)*x+(1/5)*y-(2/5) = 0| (1/3)*x+3*y-(44/3) = 0
  • We try to solve the equation: (1/3)*x+(1/5)*y-(2/5) = 0
  • 1/3*x+1/5*y-2/5 = 0 // - 1/3*x-2/5
  • 1/5*y = -(1/3*x-2/5) // : 1/5
  • y = (-(1/3*x-2/5))/1/5
  • y = 5*(2/5-(1/3*x))
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| 3*5*(2/5-(1/3*x))+(1/3)*x-(44/3) = 0| y = 5*(2/5-(1/3*x))
  • 15*(2/5-1/3*x)+x/3-44/3 = 0
  • 6-14/3*x-44/3 = 0
  • -14/3*x-26/3 = 0
  • -14/3*x-26/3 = 0 // + 26/3
  • -14/3*x = 26/3 // : -14/3
  • x = 26/3/(-14/3)
  • x = -13/7
  • We insert the solution into one of the initial equations of our system of equations
  • For y = 5*(2/5-(1/3*x)): 
  • y = 5*(2/5-(-13/7*1/3))
  • y = 5*(2/5+13/21)
  • y = 107/105*5
  • y = 107/21
  • We get a system of equations:
  • /| y = 107/21| x = -13/7

 

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