The problem requires us to solve a system of two linear equations by graphing. The equations are: $y = -x + 4$ $x + y = -\frac{7}{2}$

1. Problem Description

The problem requires us to solve a system of two linear equations by graphing. The equations are:

$y = -x + 4$

$x + y = -\frac{7}{2}$

2. Solution Steps

First, let's analyze the given equations:

Equation 1: $y = -x + 4$

This equation is in slope-intercept form ($y = mx + b$), where the slope $m = -1$ and the y-intercept $b = 4$.

Equation 2: $x + y = -\frac{7}{2}$

We can rewrite this equation in slope-intercept form by isolating $y$:

$y = -x - \frac{7}{2}$

Here, the slope $m = -1$ and the y-intercept $b = -\frac{7}{2} = -3.5$.

Since the slopes of both lines are the same ($-1$), the lines are parallel. Parallel lines never intersect. Therefore, there is no solution to this system of equations.

To verify the solution, we can set the two equations equal to each other:

$-x + 4 = -x - \frac{7}{2}$

Adding $x$ to both sides gives:

$4 = -\frac{7}{2}$

This is a contradiction, which confirms that the lines are parallel and there is no solution.

3. Final Answer

No solution.