1. **Problem:** Determine whether the point (3, -2) is a solution to the system of equations: $$y = 2x - 8$$ $$y = -x + 1$$ 2. **Formula and rules:** To check if a point $(x,y)$ is a solution, substitute $x$ and $y$ into each equation. If both equations hold true, the point is a solution. 3. **Substitute into first equation:** $$y = 2x - 8$$ Substitute $x=3$, $y=-2$: $$-2 = 2(3) - 8$$ $$-2 = 6 - 8$$ $$-2 = -2$$ This is true. 4. **Substitute into second equation:** $$y = -x + 1$$ Substitute $x=3$, $y=-2$: $$-2 = -3 + 1$$ $$-2 = -2$$ This is also true. 5. **Conclusion:** Since the point satisfies both equations, **(3, -2) is a solution to the system.**