Answer
Infinitely many solutions.
Work Step by Step
To solve a pair of equations in two variables graphically, first put each equation in function form, $y=f(x)$.
1. Graph the equations on a common screen.
2. Find the points of intersection of the graphs.
The solutions are the x- and y-coordinates of the points of intersection.
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$\begin{array}{ll}
-x+\frac{1}{2}y=-5\ \ /\times 2 & 2x-y=10\ \ /-2x\\
-2x+y=-10\ \ /+2x & -y=-2x+10\ \ /\div(-1)\\
y=2x-10 & y=2x-10\\
&
\end{array}$
1. No need to graph, since...
(but we did, anyway, see below)
2. ...the two equations have the same graph.
Infinitely many solutions.