The system shown has ___ solution(s) \( \begin{array}{l}y=\frac{1}{2} x+1 \\ 2 y-x=2 \\ \text { infinite } \\ \text { no } \\ \text { one }\end{array} \)

To determine the number of solutions for the given system of equations, let's compare the two equations you provided. The first equation is in slope-intercept form, while the second can be rewritten to identify its slope and intercept. If both equations represent the same line, they will have infinitely many solutions. If they intersect at one point, they have a single solution. If they are parallel and different, there will be no solutions. After simplifying them, if we find out that both equations are equivalent, then the system has infinite solutions. If they have different slopes, they intersect at one unique point, giving one solution. If they have the same slope but different y-intercepts, the system has no solutions. Check those slopes and intercepts to find out!