1. **State the problem:** Solve the system of equations using the substitution method: $$4x + y = 17 \quad (1)$$ $$2x + y = 9 \quad (2)$$ 2. **Isolate one variable:** From equation (2), isolate $y$: $$y = 9 - 2x$$ 3. **Substitute into the other equation:** Substitute $y = 9 - 2x$ into equation (1): $$4x + (9 - 2x) = 17$$ 4. **Simplify and solve for $x$:** $$4x + 9 - 2x = 17$$ $$\cancel{4x} + 9 - \cancel{2x} = 17 \implies 2x + 9 = 17$$ $$2x = 17 - 9$$ $$2x = 8$$ $$x = \frac{8}{2}$$ $$x = 4$$ 5. **Find $y$ using $x=4$:** Substitute $x=4$ into $y = 9 - 2x$: $$y = 9 - 2(4)$$ $$y = 9 - 8$$ $$y = 1$$ **Final answer:** $$x = 4, \quad y = 1$$