System of linear-quadratic equations

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Introduction
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
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Examples
Lessons
  1. Case 1: System with 2 Solutions
    1. Solve the system:
      y=−x+1y = - x + 1
      y=x2+x−2y = {x^2} + x - 2
    2. Verify the solutions graphically
  2. Case 2: System with 1 Solution
    1. Solve the system:
      2x−y=82x - y = 8
      y=x2−4x+1y = {x^2} - 4x + 1
    2. Verify the solutions graphically
  3. Case 3: System with No Solutions
    1. Solve the system:
      10x+5y+15=010x + 5y + 15 = 0
      y=x2−4x+2y = {x^2} - 4x + 2
    2. Verify the solutions graphically
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Topic Notes
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.
Basic Concepts
Related Concepts