1/5x+1/2y=1/10;1/5x+3y=13/5

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

Solution for 1/5x+1/2y=1/10;1/5x+3y=13/5 system of equations: 


  • /| (1/5)*x+(1/2)*y-(1/10) = 0| (1/5)*x+3*y-(13/5) = 0
  • We try to solve the equation: (1/5)*x+(1/2)*y-(1/10) = 0
  • 1/5*x+1/2*y-1/10 = 0 // - 1/5*x-1/10
  • 1/2*y = -(1/5*x-1/10) // : 1/2
  • y = (-(1/5*x-1/10))/1/2
  • y = 2*(1/10-(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*3*(1/10-(1/5*x))+(1/5)*x-(13/5) = 0| y = 2*(1/10-(1/5*x))
  • 6*(1/10-1/5*x)+x/5-13/5 = 0
  • 3/5-x-13/5 = 0
  • -x-2 = 0
  • -x-2 = 0 // + 2
  • -x = 2 // * -1
  • x = -2
  • We insert the solution into one of the initial equations of our system of equations
  • For y = 2*(1/10-(1/5*x)): 
  • y = 2*(1/10-(-2*1/5))
  • y = 2*(1/10+2/5)
  • y = 1/2*2
  • y = 1
  • We get a system of equations:
  • /| y = 1| x = -2

 

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