1. **State the problem:** We need to solve the simultaneous equations: $$y = -2x + 11$$ $$y = 0.5x + 2.25$$ 2. **Use the substitution method:** Since both expressions equal $y$, set them equal to each other: $$-2x + 11 = 0.5x + 2.25$$ 3. **Solve for $x$:** Move all $x$ terms to one side and constants to the other: $$-2x - 0.5x = 2.25 - 11$$ $$-2.5x = -8.75$$ Divide both sides by $-2.5$: $$x = \frac{-8.75}{-2.5} = 3.5$$ 4. **Find $y$ by substituting $x=3.5$ into one of the original equations:** Using $y = 0.5x + 2.25$: $$y = 0.5(3.5) + 2.25 = 1.75 + 2.25 = 4$$ 5. **Final answer:** The solution to the simultaneous equations is: $$(x, y) = (3.5, 4)$$ This means the two lines intersect at the point $(3.5, 4)$ on the graph.