1. **Problem Statement:** We are given three lines representing walkways in a park: $$x + y - 4 = 0$$ $$2x - y - 2 = 0$$ $$x - 2y + 2 = 0$$ We need to find the coordinates of the points where these lines intersect. 2. **Understanding the problem:** The intersection points of the lines are the solutions to the pairs of equations taken two at a time. Since the lines form a triangle, each pair intersects at a unique point. 3. **Step 1: Find intersection of line 1 and line 2:** Equations: $$x + y - 4 = 0 \implies y = 4 - x$$ $$2x - y - 2 = 0$$ Substitute $y$ from the first into the second: $$2x - (4 - x) - 2 = 0$$ $$2x - 4 + x - 2 = 0$$ $$3x - 6 = 0$$ $$3x = 6 \implies x = 2$$ Then, $$y = 4 - 2 = 2$$ So, intersection point is $(2, 2)$. 4. **Step 2: Find intersection of line 2 and line 3:** Equations: $$2x - y - 2 = 0 \implies y = 2x - 2$$ $$x - 2y + 2 = 0$$ Substitute $y$ into the third equation: $$x - 2(2x - 2) + 2 = 0$$ $$x - 4x + 4 + 2 = 0$$ $$-3x + 6 = 0$$ $$-3x = -6 \implies x = 2$$ Then, $$y = 2(2) - 2 = 4 - 2 = 2$$ Intersection point is $(2, 2)$. 5. **Step 3: Find intersection of line 1 and line 3:** Equations: $$x + y - 4 = 0 \implies y = 4 - x$$ $$x - 2y + 2 = 0$$ Substitute $y$ into the third equation: $$x - 2(4 - x) + 2 = 0$$ $$x - 8 + 2x + 2 = 0$$ $$3x - 6 = 0$$ $$3x = 6 \implies x = 2$$ Then, $$y = 4 - 2 = 2$$ Intersection point is $(2, 2)$. 6. **Conclusion:** All three lines intersect at the same point $(2, 2)$, so the walkways meet at this single point. **Final answer:** The coordinates of the point of intersection of the walkways are $$\boxed{(2, 2)}$$.