How do you approach a simultaneous equations problem?

There should be at least as many simultaneous equations as there are unknown variables - or else you cannot get a numerical answer! Start by trying to eliminate one of the variables. You can multiply the equation by an integer to eliminate variables but remember to multiply both sides! Then subsitiute the value you have found back into one of the original equations. This will give you your answer.

Example:

4x+2y+z=11    (1)

3x+2y+2z=13     (2)

x+y+z=6    (3)

First, do (2)-(1), giving -x+z=2, and hence z=x+2

Then subsitute this into (3). This gives x+y+x+2=6, 2x+y=4 (4). If you double (4), you get 4x+2y=8 (5). Then do (1)-(5) to get z=3. We know z=x+2, so x=1. If we substitute both of these into (3), we find y=2. Thus this set of equations is solved.