There are two types of simultaneous equations:

• Both equations are linear
• One equation is linear, and the other is quadratic

Both equations are linear (link to GCSE)

These can be solved by using elimination or substitution. There will be one pair of solutions.

One equation is linear, and the other is quadratic

These must be solved using substitution, by substituting a variable from the linear equation into the quadratic equation. There will be two pairs of solutions.

Simultaneous equations can also be solved graphically

The points of intersection on a graph represent the solutions to a pair of simultaneous equations.

Tip: Watch out for discriminant questions which are often combined with this topic. For example, you might have a line and a curve which do not intersect (i.e., no solutions), or a line which just touches a curve (i.e., one solution) or a line which does intersects a curve (i.e., two solutions).