System of quadratic-quadratic equations

System of quadratic-quadratic equations

The solutions to a system of equations are the points of intersection of the lines. For a system with two quadratic equations, there are 4 cases to consider: 2 solutions, 1 solution, no solutions, and infinite solutions.

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

  • 2.
    Case 1: System with 2 Solutions
    Solve the system, then verify the solutions graphically:
    y=x26x+5y = {x^2} - 6x + 5
    y=2x2+9x7y = - 2{x^2} + 9x - 7

  • 3.
    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

  • 4.
    Case 3: System with No Solutions
    Solve the system, then verify the solutions graphically:
    y=x2+6x10y = - {x^2} + 6x - 10
    y=2x2+6x+5y = 2{x^2} + 6x + 5

  • 5.
    Case 4: System with Infinite Solutions
    Solve the system, then verify the solutions graphically:
    x24xy+3=0{x^2} - 4x - y + 3 = 0
    5y5x2+20x15=05y - 5{x^2} + 20x - 15 = 0