Solve the following system of equations graphically on the set of axes below. \[ \begin{array}{l} y=\frac{1}{2} x-5 \\ x+y=1\end{array} \]

To solve the system of equations graphically, you can plot both equations on a coordinate plane: The first equation is \(y = \frac{1}{2} x - 5\). This is a straight line with a slope of \(\frac{1}{2}\) and a y-intercept of \(-5\). To plot this line, start at the y-intercept at \((0, -5)\). From this point, you can move up 1 unit and right 2 units to find another point, which gives you the coordinates \((2, -4)\). You can plot more points if needed, but two should be sufficient for a straight line. The second equation, \(x + y = 1\), can be rewritten as \(y = 1 - x\). This line has a slope of \(-1\) and a y-intercept of \(1\). Begin at the y-intercept \((0, 1)\) and go down 1 unit and right 1 unit to get to the point \((1, 0)\). Again, you can plot more points, like \((2, -1)\). Once you have both lines plotted, look for the point where they intersect. This intersection point will be the solution to the system of equations. When you find the intersection, you'll find the coordinates of the solution \((x,y)\). In this case, the two lines will intersect at the point \((-4, 5)\). Thus, the solution to the system is \(x = -4\) and \(y = 5\).