y=x^2-3;y=x+1

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x+3y=14

Solution for y=x^2-3;y=x+1 system of equations: 


  • /| y-x^2+3 = 0| y-x-1 = 0
  • We try to solve the equation: y-x^2+3 = 0
  • y-x^2+3 = 0 // - 3-x^2
  • y = -(3-x^2)
  • y = x^2-3
  • We insert the solution into one of the initial equations of our system of equations
  • We get a system of equations:
  • /| x^2-x-3-1 = 0| y = x^2-3
  • x^2-x-4 = 0
  • DELTA = (-1)^2-(-4*1*4)
  • DELTA = 17
  • DELTA > 0, so the uquation has 2 solutions
  • x = (17^(1/2)+1)/(1*2) or x = (1-17^(1/2))/(1*2)
  • x = (17^(1/2)+1)/2 or x = (1-17^(1/2))/2
  • We insert the solution into one of the initial equations of our system of equations
  • 1) For x = (1-17^(1/2))/2
  • For y = x^2-3: 
  • y = ((1-17^(1/2))/2)^2-3
  • y = ((1-(1*17^(1/2)))/2)^2-3
  • y = ((1-17^(1/2))/2)^2-3
  • y = ((1-17^(1/2))^2)/4-3
  • We get a system of equations:
  • /| y = ((1-17^(1/2))^2)/4-3| x = (1-17^(1/2))/2
  • 2) For x = (17^(1/2)+1)/2
  • For y = x^2-3: 
  • y = ((17^(1/2)+1)/2)^2-3
  • y = ((1*17^(1/2)+1)/2)^2-3
  • y = ((17^(1/2)+1)/2)^2-3
  • y = ((17^(1/2)+1)^2)/4-3
  • We get a system of equations:
  • /| y = ((17^(1/2)+1)^2)/4-3| x = (17^(1/2)+1)/2

 

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