1. **State the problem:** We need to identify which graph correctly represents the system of linear equations: $$y = -x + 2$$ $$y = \frac{1}{2}x + 2$$ 2. **Understand the equations:** Both lines have a y-intercept at 2. - The first line has a slope of $-1$, meaning it goes down 1 unit for every 1 unit it moves right. - The second line has a slope of $\frac{1}{2}$, meaning it goes up 0.5 units for every 1 unit it moves right. 3. **Analyze the graphs:** - The correct graph should show two lines intersecting at the point where $x=0$ and $y=2$ (the y-intercept). - One line should slope downward (negative slope), the other upward but less steep (positive slope of $\frac{1}{2}$). 4. **Conclusion:** The top-left graph matches these conditions because: - Both lines cross the y-axis at 2. - One line has a negative slope (downward), the other has a positive slope of about $\frac{1}{2}$. Therefore, the graphic solution of the system is shown in the **top-left graph**.