System of quadratic-quadratic equations

Intros
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Lessons
  1. • 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=ax2+bx+cy = a{x^2} + bx + c
    quadratic equation: y=dx2+ex+fy = 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

    System of quadratic-quadratic equations with 2 solutions

    System of quadratic-quadratic equations with one solution

    System of quadratic-quadratic equations with no solution

    System of quadratic-quadratic equations with infinite solutions
Examples
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Lessons
  1. Case 1: System with 2 Solutions
    Solve the system, then verify the solutions graphically:
    y=x2−6x+5y = {x^2} - 6x + 5
    y=−2x2+9x−7y = - 2{x^2} + 9x - 7
  2. Case 2: System with 1 Solution
    Solve the system, then verify the solutions graphically:
    y=2x2+6x+7y = 2{x^2} + 6x + 7
    y=−x2+4y = - {x^2} + 4
  3. Case 3: System with No Solutions
    Solve the system, then verify the solutions graphically:
    y=−x2+6x−10y = - {x^2} + 6x - 10
    y=2x2+6x+5y = 2{x^2} + 6x + 5
  4. Case 4: System with Infinite Solutions
    Solve the system, then verify the solutions graphically:
    x2−4x−y+3=0{x^2} - 4x - y + 3 = 0
    5y−5x2+20x−15=05y - 5{x^2} + 20x - 15 = 0