1. **State the problem:** Solve the system of equations by graphing and find the point of intersection. The system is: $$y=2x-3$$ $$y=-3x+2$$ 2. **Recall the method:** The solution to the system is the point where the two lines intersect, meaning the values of $x$ and $y$ satisfy both equations simultaneously. 3. **Set the equations equal to find the intersection:** $$2x - 3 = -3x + 2$$ 4. **Solve for $x$:** $$2x - 3 = -3x + 2$$ $$2x + 3x = 2 + 3$$ $$5x = 5$$ $$x = \cancel{\frac{5}{5}}1$$ 5. **Substitute $x=1$ into one of the original equations to find $y$:** Using $y=2x-3$: $$y = 2(1) - 3 = 2 - 3 = -1$$ 6. **Conclusion:** The point of intersection is at $$\boxed{(1, -1)}$$ This means the two lines cross at the point $(1, -1)$ on the graph.