Identify an equation which can be obtained from the following system by
eliminating one of the variables.
\[ \begin{alignedat}{80}
&y^{2} & - &2 &x & + &3 & = 0 & & & & & & & &
\\ &x & - & &y & - &1 & = 0 & & & & & & & &
\\\end{alignedat}\]
Find a number which is a sum of one half of the bigger solution of
\[
x^{2} - 10x + 24 = 0
\]
and a double of the smaller solution of
\[
-x^{2} + 10x - 16 = 0.
\]