1. **State the problem:** Solve the system of linear 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 $x$:** $$4x + 9 - 2x = 17$$ $$2x + 9 = 17$$ $$2x = 17 - 9$$ $$2x = 8$$ 5. **Divide both sides by 2:** $$\cancel{2}x = \cancel{2}4$$ $$x = 4$$ 6. **Find $y$ by substituting $x=4$ back into $y = 9 - 2x$:** $$y = 9 - 2(4)$$ $$y = 9 - 8$$ $$y = 1$$ **Final answer:** $$x = 4, \quad y = 1$$