1. The problem is to solve a system of equations using the graphical method. 2. The graphical method involves plotting each equation on the same coordinate plane and finding the point(s) where the graphs intersect. 3. The intersection point(s) represent the solution(s) to the system. 4. For example, consider the system: $$y = 2x + 1$$ $$y = -x + 4$$ 5. Plot the first line by finding points that satisfy $y = 2x + 1$. 6. Plot the second line by finding points that satisfy $y = -x + 4$. 7. The intersection point of these two lines is the solution to the system. 8. To find the intersection algebraically, set the right sides equal: $$2x + 1 = -x + 4$$ 9. Solve for $x$: $$2x + x = 4 - 1$$ $$3x = 3$$ $$x = 1$$ 10. Substitute $x=1$ into one of the equations to find $y$: $$y = 2(1) + 1 = 3$$ 11. Therefore, the solution is the point $(1, 3)$, which is the intersection of the two lines. 12. Graphically, this point is where the two lines cross on the coordinate plane.