Find the solution set of the two equations and .
The first equation can be rearranged to give
Substituting into the second equation gives
which can be rearranged to
This is a quadratic equation in the variable . Making the substitution enables this to be seen more easily.
This equation can be solved by factorisation.
But as , it must have a positive value. Therefore . Hence it follows that
Substituting this value of into the first equation gives
Therefore, the solution set is .