Simultaneous equations (one linear, one quadratic)

What you'll learn

1. 1

   Imagine you have two magic boxes. One box gives you a straight line (y = x + 2), and the other gives you a curve (y = x²).

2. 2

   What are we looking for when we solve two equations together?

3. 3

   Let's solve y = x + 2 and y = x² together. We find where they cross.

4. 4

   Now you try! Solve y = 2x + 1 and y = x². Drag the x-values to the correct spots.

5. 5

   When solving y = 2x + 1 and y = x², what equation do you get after setting them equal?

6. 6

   Let's check your answer. If x = -1, does it work in both equations?

7. 7

   Find the other solution. Solve x² = 2x + 1 by dragging the x-value on the number line.

8. 8

   What are the two solutions to y = 2x + 1 and y = x²?