1/3x+1/5y=-17/15;1/3x+3y=5/3

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

Solution for 1/3x+1/5y=-17/15;1/3x+3y=5/3 system of equations: 


  • /| (1/3)*x+(1/5)*y-(-17/15) = 0| (1/3)*x+3*y-(5/3) = 0
  • We try to solve the equation: (1/3)*x+(1/5)*y-(-17/15) = 0
  • 1/3*x+1/5*y+17/15 = 0 // - 1/3*x+17/15
  • 1/5*y = -(1/3*x+17/15) // : 1/5
  • y = (-(1/3*x+17/15))/1/5
  • y = -5*(1/3*x+17/15)
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| (1/3)*x-5*3*(1/3*x+17/15)-(5/3) = 0| y = -5*(1/3*x+17/15)
  • x/3-15*(1/3*x+17/15)-5/3 = 0
  • -14/3*x-17-5/3 = 0
  • -14/3*x-56/3 = 0
  • -14/3*x-56/3 = 0 // + 56/3
  • -14/3*x = 56/3 // : -14/3
  • x = 56/3/(-14/3)
  • x = -4
  • We insert the solution into one of the initial equations of our system of equations
  • For y = -5*(1/3*x+17/15): 
  • y = -5*(17/15-4*1/3)
  • y = -5*(17/15-4/3)
  • y = -5*(-1/5)
  • y = 1/5*5
  • y = 1
  • We get a system of equations:
  • /| y = 1| x = -4

 

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