There are two types of simultaneous equations: [ul]liBoth equations are linear[/li]liOne equation is linear, and the other is quadratic[/li]/uluBoth equations are linear (link to GCSE)/u

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

uOne equation is linear, and the other is quadratic/u

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.

[b]uSimultaneous equations can also be solved graphically[/u]/b

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

Tip: Watch out for topic=2/9discriminant/topic questions which are often combined with this topic. For example, you might have a line and a curve which bdo not intersect/b (i.e., no solutions), or a line which just btouches/b a curve (i.e., one solution) or a line which bdoes intersects/b a curve (i.e., two solutions).

Simultaneous equations involving one linear equation and one quadratic equation are solved by substituting a variable from the linear equation into the quadratic equation.

Remember that there will be btwo pairs/b of solutions!