1. **State the problem:** We are given the system of equations: $$y = -x + 2$$ $$y = 2 - x$$ We need to graph the system and find its solution. 2. **Analyze the equations:** Notice that both equations are actually the same because: $$-x + 2 = 2 - x$$ This means both lines represent the same line. 3. **Graphing the system:** Since both equations represent the same line, the graph will show one line passing through points such as $(0, 2)$, $(2, 0)$, and $(-2, 4)$. 4. **Solution of the system:** Because the two equations are identical, every point on the line satisfies both equations. Therefore, the system has **infinitely many solutions**. **Final answer:** The system has infinitely many solutions because the two equations represent the same line.