The problem asks to solve the system of equations $y = -x + 3$ and $x + y = \frac{5}{2}$. We need to determine if the system has a unique solution, infinitely many solutions, or no solution.

1. Problem Description

The problem asks to solve the system of equations $y = -x + 3$ and $x + y = \frac{5}{2}$. We need to determine if the system has a unique solution, infinitely many solutions, or no solution.

2. Solution Steps

We have two equations:

$y = -x + 3$

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

Substitute the first equation into the second equation:

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

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

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

Since $3 \neq \frac{5}{2}$, the equation is false.

This means that the two lines are parallel and do not intersect. Therefore, there is no solution to the system of equations.

3. Final Answer

C. There is no solution.