One of the reasons that graphical representation of equations is useful is that it allows us to find approximate solutions to systems of equations. The solutions are represented by the intersections points of the graphs. Typically with simple equations it is easier to solve them algebraically, but some equations are too difficult to solve algebraically, which is why we also need to have in our toolkit the ability to solve them graphically.

Example

1. Use a graph to solve the equation 3x² + 5 = 2x + 10

2. Add a line to your original graph to solve 3x² + 5 = 7

Exercise

Let’s complete exercise 16 from pages 66 and 67 of the core textbook:

The answers are below: