We have y= two expressions in x, therefore the two expressions are equal, so effectively using substitution we have:
(1/2)x+2=(1/4)x-8, (1/4)x=-10 and x=-40. We can now calculate y: y=(1/2)x+2=-20+2=-18 or y=(1/4)x-8=-10-8=-18.
Solution is x=-40, y=-18, one solution.
The question could be interpreted: y=1/(2x)+2, y=1/(4x)-8, in which case the solution is x=-1/40, y=-1/18.
Another way to solve the system is to use a graph, plotting the two equations on the same graph; where the graphs intersect is the solution as a point (x,y)=(-40,-18) (or (-1/40,-1/18), depending on interpretation).