1x1y=9;1x-3y=-3

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Remember to put linear equations with variables x and y.
for example:
2x+y=8
x+3y=14

Solution for 1x1y=9;1x-3y=-3 system of equations: 


  • /| 1*x^1*y-9 = 0| 1*x-(3*y)+3 = 0
  • We try to solve the equation: 1*x^1*y-9 = 0
  • x*y-9 = 0 // + 9
  • x*y = 9 // : x
  • y = 9/x
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| 1*x-(3*(9/x))+3 = 0| y = 9/x
  • 1*x^1-27*x^-1+3*x^0 = 0
  • (1*x^2+3*x^1-27*x^0)/(x^1) = 0 // * x^2
  • x^1*(1*x^2+3*x^1-27*x^0) = 0
  • 0 nie naleu017Cy do dziedziny, wiu0119c mou017Cemy pominu0105u0107 fragment: x^1
  • x^2+3*x-27 = 0
  • x^2+3*x-27 = 0
  • DELTA = 3^2-(-27*1*4)
  • DELTA = 117
  • DELTA > 0, so the uquation has 2 solutions
  • x = (117^(1/2)-3)/(1*2) or x = (-117^(1/2)-3)/(1*2)
  • x = (3*13^(1/2)-3)/2 or x = (-3*13^(1/2)-3)/2
  • x in { (-3*13^(1/2)-3)/2, (3*13^(1/2)-3)/2} 
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = (-3*13^(1/2)-3)/2
  • For y = 9/x: 
  • y = 9/((-3*13^(1/2)-3)/2)
  • y = 9/((-3*1*13^(1/2)-3)/2)
  • y = 9/((-3*13^(1/2)-3)/2)
  • y = 18*(-3*13^(1/2)-3)^-1
  • We get a system of equations:
  • /| y = 18*(-3*13^(1/2)-3)^-1| x = (-3*13^(1/2)-3)/2
  • 2) For x = (3*13^(1/2)-3)/2
  • For y = 9/x: 
  • y = 9/((3*13^(1/2)-3)/2)
  • y = 9/((1*3*13^(1/2)-3)/2)
  • y = 9/((3*13^(1/2)-3)/2)
  • y = 18*(3*13^(1/2)-3)^-1
  • We get a system of equations:
  • /| y = 18*(3*13^(1/2)-3)^-1| x = (3*13^(1/2)-3)/2

 

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