1. **State the problem:** Solve the simultaneous equations: $$4x + y = 14$$ $$x + 5y = 13$$ 2. **Formula and method:** We will use the substitution or elimination method to solve these linear equations. 3. **Step 1: Express $y$ from the first equation:** $$y = 14 - 4x$$ 4. **Step 2: Substitute $y$ into the second equation:** $$x + 5(14 - 4x) = 13$$ 5. **Step 3: Simplify and solve for $x$:** $$x + 70 - 20x = 13$$ $$-19x + 70 = 13$$ $$-19x = 13 - 70$$ $$-19x = -57$$ $$x = \frac{-57}{-19} = 3$$ 6. **Step 4: Substitute $x=3$ back into $y = 14 - 4x$ to find $y$:** $$y = 14 - 4(3) = 14 - 12 = 2$$ 7. **Final answer:** The solution to the simultaneous equations is $$x = 3, \quad y = 2$$