System of linear-quadratic equations

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
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
?
Examples
Lessons
  1. Case 1: System with 2 Solutions
    1. Solve the system:
      y=x+1y = - x + 1
      y=x2+x2y = {x^2} + x - 2
    2. Verify the solutions graphically
  2. Case 2: System with 1 Solution
    1. Solve the system:
      2xy=82x - y = 8
      y=x24x+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=x24x+2y = {x^2} - 4x + 2
    2. Verify the solutions graphically