x*y=42;x-y=11

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

Solution for x*y=42;x-y=11 system of equations: 


  • /| x*y-42 = 0| x-y-11 = 0
  • We try to solve the equation: x*y-42 = 0
  • x*y-42 = 0 // + 42
  • x*y = 42 // : x
  • y = 42/x
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| x-(42/x)-11 = 0| y = 42/x
  • 1*x^1-42*x^-1-11*x^0 = 0
  • (1*x^2-11*x^1-42*x^0)/(x^1) = 0 // * x^2
  • x^1*(1*x^2-11*x^1-42*x^0) = 0
  • 0 nie naleu017Cy do dziedziny, wiu0119c mou017Cemy pominu0105u0107 fragment: x^1
  • x^2-11*x-42 = 0
  • x^2-11*x-42 = 0
  • DELTA = (-11)^2-(-42*1*4)
  • DELTA = 289
  • DELTA > 0, so the uquation has 2 solutions
  • x = (289^(1/2)+11)/(1*2) or x = (11-289^(1/2))/(1*2)
  • x = 14 or x = -3
  • x in { -3, 14} 
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = -3
  • For y = 42/x: 
  • y = 42/(-3)
  • y = -14
  • We get a system of equations:
  • /| y = -14| x = -3
  • 2) For x = 14
  • For y = 42/x: 
  • y = 42/14
  • y = 3
  • We get a system of equations:
  • /| y = 3| x = 14

 

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