1/5x+1/2y=4/5;1/5x+2y=34/5

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

Solution for 1/5x+1/2y=4/5;1/5x+2y=34/5 system of equations: 


  • /| (1/5)*x+(1/2)*y-(4/5) = 0| (1/5)*x+2*y-(34/5) = 0
  • We try to solve the equation: (1/5)*x+(1/2)*y-(4/5) = 0
  • 1/5*x+1/2*y-4/5 = 0 // - 1/5*x-4/5
  • 1/2*y = -(1/5*x-4/5) // : 1/2
  • y = (-(1/5*x-4/5))/1/2
  • y = 2*(4/5-(1/5*x))
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| 2*2*(4/5-(1/5*x))+(1/5)*x-(34/5) = 0| y = 2*(4/5-(1/5*x))
  • 4*(4/5-1/5*x)+x/5-34/5 = 0
  • 16/5-3/5*x-34/5 = 0
  • -3/5*x-18/5 = 0
  • -3/5*x-18/5 = 0 // + 18/5
  • -3/5*x = 18/5 // : -3/5
  • x = 18/5/(-3/5)
  • x = -6
  • We insert the solution into one of the initial equations of our system of equations
  • For y = 2*(4/5-(1/5*x)): 
  • y = 2*(4/5-(-6*1/5))
  • y = 2*(4/5+6/5)
  • y = 2*2
  • y = 4
  • We get a system of equations:
  • /| y = 4| x = -6

 

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