System of linear-quadratic equations

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/1
?
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
0/6
?
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