The problem asks us to solve the given system of equations by graphing. The system of equations is: $y = -x + 4$ $x + y = \frac{1}{2}$

1. Problem Description

The problem asks us to solve the given system of equations by graphing. The system of equations is:

$y = -x + 4$

$x + y = \frac{1}{2}$

2. Solution Steps

First, we need to rewrite the second equation in slope-intercept form ($y = mx + b$).

$x + y = \frac{1}{2}$

$y = -x + \frac{1}{2}$

Now we have the system in slope-intercept form:

$y = -x + 4$

$y = -x + \frac{1}{2}$

Since the slopes are equal (both are $-1$) and the y-intercepts are different (4 and $\frac{1}{2}$), the lines are parallel. Parallel lines never intersect, so there is no solution to this system of equations.

3. Final Answer

No Solution.