System of linear-quadratic equations

Lessons

• Introduction
  • The solutions to a system of equations are the points of intersection of the graphs.
  • For a system consisting of a linear equation and a quadratic equation:
  linear equation: $y = mx + b$
  quadratic equation: $y = a{x^2} + bx + c$
  There are 3 cases to consider:
  
  

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

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• 1.
  Case 1: System with 2 Solutions
  a)

  Solve the system:
  $y = - x + 1$
  $y = {x^2} + x - 2$
  
  
  b)

  Verify the solutions graphically
  
  

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• 2.
  Case 2: System with 1 Solution
  a)

  Solve the system:
  $2x - y = 8$
  $y = {x^2} - 4x + 1$
  
  
  b)

  Verify the solutions graphically
  
  

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• 3.
  Case 3: System with No Solutions
  a)

  Solve the system:
  $10x + 5y + 15 = 0$
  $y = {x^2} - 4x + 2$
  
  
  b)

  Verify the solutions graphically
  
  

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