Final answer:
After graphing the equations Y = ½X + 8 and X - 4Y = -8, the solution is the point where both lines intersect. However, the intersection point (4, 10) is not listed in the provided options, suggesting an error in the question details or answer choices.
Step-by-step explanation:
To solve the system of equations graphically, we first graph each equation on a set of axes. The first equation, Y = ½X + 8, is a straight line with a slope of ½ and a y-intercept of 8. The second equation can be rearranged to the form Y = ¼X + 2, which is also a straight line, with a slope of ¼ and a y-intercept of 2.
Once both lines are graphed, the point of intersection represents the solution to the system of equations. By examining the graph or by algebraic calculation, it becomes apparent that the solution to the system is where both line equations equal each other, which occurs at the coordinates (4, 10).
However, this set of coordinates is not an option in the given multiple choice answers, which indicates there may have been a typo or miscalculation in the original student's question or potential answer choices.