System of linear-quadratic equations

System of linear-quadratic equations

The solutions to a system of equations are the points of intersection of their graphs. There are 3 cases you will come across when trying to solve the system. There can be 2 solutions, 1 solution or even no solutions.

Lessons

  • 1.
    • 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+by = mx + b
    quadratic equation: y=ax2+bx+cy = a{x^2} + bx + c
    There are 3 cases to consider:

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

    System of linear-quadratic equations with two solutions

    System of linear-quadratic equations with one solution

    System of linear-quadratic equations no solution

  • 2.
    Case 1: System with 2 Solutions
    a)
    Solve the system:
    y=x+1y = - x + 1
    y=x2+x2y = {x^2} + x - 2

    b)
    Verify the solutions graphically


  • 3.
    Case 2: System with 1 Solution
    a)
    Solve the system:
    2xy=82x - y = 8
    y=x24x+1y = {x^2} - 4x + 1

    b)
    Verify the solutions graphically


  • 4.
    Case 3: System with No Solutions
    a)
    Solve the system:
    10x+5y+15=010x + 5y + 15 = 0
    y=x24x+2y = {x^2} - 4x + 2

    b)
    Verify the solutions graphically


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