We are asked to solve the following system of linear equations by graphing: $y = -x + 4$ $x + y = -\frac{1}{2}$

1. Problem Description

We are asked to solve the following system of linear equations by graphing:

$y = -x + 4$

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

2. Solution Steps

First, we rewrite the second equation to isolate y:

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

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

Now we have two equations in slope-intercept form ($y = mx + b$):

$y = -x + 4$

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

The first equation has a slope of -1 and a y-intercept of

4. The second equation has a slope of -1 and a y-intercept of $-\frac{1}{2}$.

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

3. Final Answer

No solution.