The problem asks us to solve the system of equations $y = -x + 3$ $x + y = -\frac{5}{2}$ by graphing. We need to find the point of intersection of the two lines.

1. Problem Description

The problem asks us to solve the system of equations

$y = -x + 3$

$x + y = -\frac{5}{2}$

by graphing. We need to find the point of intersection of the two lines.

2. Solution Steps

First, we have the equation $y = -x + 3$. This is a linear equation in slope-intercept form, where the slope is $-1$ and the y-intercept is $3$. We can also find the x-intercept by setting $y=0$ which gives $0 = -x + 3$, or $x=3$. So, we have two points (0, 3) and (3, 0).

Next, let's rewrite the second equation $x + y = -\frac{5}{2}$ in slope-intercept form:

$y = -x - \frac{5}{2}$

This is a linear equation in slope-intercept form, where the slope is $-1$ and the y-intercept is $-\frac{5}{2} = -2.5$. We can find the x-intercept by setting $y=0$ which gives $x = -\frac{5}{2} = -2.5$. So we have two points (0, -2.5) and (-2.5, 0).

Now we have the two lines. To find the intersection point, we can set the two equations equal to each other:

$-x + 3 = -x - \frac{5}{2}$

$3 = -\frac{5}{2}$

This is impossible, therefore, the two lines are parallel and there is no solution.

Alternatively, we can solve the system algebraically.

$y = -x + 3$

$x + y = -\frac{5}{2}$

Substitute the first equation into the second:

$x + (-x + 3) = -\frac{5}{2}$

$3 = -\frac{5}{2}$

This is a contradiction, indicating that the system has no solution. This confirms the lines are parallel.

3. Final Answer

No solution