1. **State the problem:** Solve the system of equations by graphing: $$y=3x-7$$ $$y=-x+1$$ Determine if the system has one solution, infinitely many solutions, or no solution. 2. **Recall the method:** When solving by graphing, each equation represents a line. The solution(s) correspond to the point(s) where the lines intersect. 3. **Graph each line:** - For $$y=3x-7$$, the slope is 3 and the y-intercept is -7. - For $$y=-x+1$$, the slope is -1 and the y-intercept is 1. 4. **Find the intersection algebraically to confirm:** Set the right sides equal: $$3x - 7 = -x + 1$$ 5. **Solve for $$x$$:** $$3x + x = 1 + 7$$ $$4x = 8$$ $$x = \frac{8}{4}$$ $$x = 2$$ 6. **Find $$y$$ by substituting $$x=2$$ into one of the equations:** $$y = 3(2) - 7 = 6 - 7 = -1$$ 7. **Conclusion:** The lines intersect at the point $$(2, -1)$$, so the system has exactly one solution. **Final answer:** The system has one solution at $$(2, -1)$$.