Simultaneous Equations 2

When solving simultaneous equations, particularly complicated ones that include a quadratic, it’s always a good idea to consider what the equations look like on a graph. You should recall that the point, or points, where two lines (or curves) intersect is a solution to the system of simultaneous equations. If you can sketch out the curve and the straight line, it will give you an indication of how many solutions there are, and their approximate position on the grid.

When both the equations you are solving simultaneously are linear, you have a choice of methods – elimination or substitution. However, when one of these equations is a quadratic you can ONLY use the substitution method. You have to substitute the linear equation (possibly rearranging it first) into the quadratic, and then solve the quadratic. Remember this will give you up to two possible solutions. Substitute each of these solutions back into the LINEAR equation to find the corresponding value of the other variable.

You’re not quite finished yet – the final thing is to check that each pair of values fits BOTH equations. If one doesn’t then it isn’t a valid solution, and you should discard it (but always explain why!). Only now can you say ‘job done’!