1. **State the problem:** Solve the system of linear equations: $$4x + 5y = 14$$ $$2x + 5y = 2$$ 2. **Formula and method:** We will use the elimination method to solve for $x$ and $y$. The goal is to eliminate one variable by subtracting the equations. 3. **Subtract the second equation from the first:** $$\begin{aligned} (4x + 5y) - (2x + 5y) &= 14 - 2 \\ 4x + 5y - 2x - 5y &= 12 \\ (4x - 2x) + (5y - 5y) &= 12 \\ 2x + \cancel{5y} - \cancel{5y} &= 12 \\ 2x &= 12 \end{aligned}$$ 4. **Solve for $x$:** $$x = \frac{12}{2} = 6$$ 5. **Substitute $x=6$ into one of the original equations to find $y$:** Using the second equation: $$2(6) + 5y = 2$$ $$12 + 5y = 2$$ 6. **Isolate $y$:** $$5y = 2 - 12$$ $$5y = -10$$ 7. **Solve for $y$:** $$y = \frac{-10}{5} = -2$$ **Final answer:** $$x = 6, \quad y = -2$$