1. **Problem statement:** We are given the system of equations: $$y = 3x + 2$$ $$y = x - 2$$ We want to solve this system graphically and algebraically. 2. **Graphical solution:** - Plot both lines on the coordinate system. - The solution is the point where the two lines intersect. 3. **Algebraic solution:** - Since both expressions equal $y$, set them equal to each other: $$3x + 2 = x - 2$$ 4. **Solve for $x$:** $$3x + 2 = x - 2$$ $$3x - x = -2 - 2$$ $$2x = -4$$ $$x = \frac{\cancel{2}x}{\cancel{2}} = \frac{-4}{2} = -2$$ 5. **Find $y$ by substituting $x = -2$ into one of the original equations:** $$y = 3(-2) + 2 = -6 + 2 = -4$$ 6. **Answer:** The solution to the system is the point $$\boxed{(-2, -4)}$$ This means the two lines intersect at $x = -2$ and $y = -4$.