1. **State the problem:** Solve the simultaneous equations: $$4x + y = 9$$ $$x - y = 1$$ 2. **Formula and rules:** We can solve simultaneous equations by substitution or elimination. Here, substitution is straightforward. 3. **Step 1: Express $y$ from the second equation:** $$x - y = 1 \implies y = x - 1$$ 4. **Step 2: Substitute $y = x - 1$ into the first equation:** $$4x + (x - 1) = 9$$ 5. **Step 3: Simplify and solve for $x$:** $$4x + x - 1 = 9$$ $$5x - 1 = 9$$ $$5x = 9 + 1$$ $$5x = 10$$ 6. **Step 4: Divide both sides by 5:** $$\cancel{5}x = \frac{10}{\cancel{5}}$$ $$x = 2$$ 7. **Step 5: Substitute $x=2$ back into $y = x - 1$ to find $y$:** $$y = 2 - 1 = 1$$ **Final answer:** $$x = 2, \quad y = 1$$ This means the solution to the system is the point $(2,1)$ where both equations are true.