3.1 linear simultaneous equations, 3.2 quadratic simultaneous equations and 3.3 simultaneous equations on graph

How can linear simultaneous equations be solved?

Using elimination or substitution

Example 1

Example 2

How do you solve simultaneous equations involving one linear equation and one quadratic equation?

You need to use substitution

How many solutions can simultaneous equations involving one linear equation and one quadratic equation have?

They can have up to two pairs of solutions

Example 3

On a graph, what are the solutions to a pair of simultaneous equations?

The points of intersection of their graphs

Example 4

Example 5

How can the graph of a linear equation and graph of a quadratic graph intersect?

• Intersect twice

• Intersect once

• Not intersect

after substituting, how can you determine how many points of intersection there are?

Using the discriminant

Example 6