System of quadratic-quadratic equations

Lessons

• Introduction
  • The solutions to a system of equations are the points of intersection of the graphs.
  • For a system consisting of two quadratic equations:
  quadratic equation: $y = a{x^2} + bx + c$
  quadratic equation: $y = d{x^2} + ex + f$
  There are 4 cases to consider:

  case 1: 2 solutions	case 2: 1 solution	case 3: no solutions	case 4: infinite solutions

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• 1.
  Case 1: System with 2 Solutions
  Solve the system, then verify the solutions graphically:
  $y = {x^2} - 6x + 5$
  $y = - 2{x^2} + 9x - 7$
  

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• 2.
  Case 2: System with 1 Solution
  Solve the system, then verify the solutions graphically:
  $y = 2{x^2} + 6x + 7$
  $y = - {x^2} + 4$
  

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• 3.
  Case 3: System with No Solutions
  Solve the system, then verify the solutions graphically:
  $y = - {x^2} + 6x - 10$
  $y = 2{x^2} + 6x + 5$
  

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• 4.
  Case 4: System with Infinite Solutions
  Solve the system, then verify the solutions graphically:
  ${x^2} - 4x - y + 3 = 0$
  $5y - 5{x^2} + 20x - 15 = 0$
  

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