1. **State the problem:** Solve the system of linear equations: $$4x - 5y = -3$$ $$14x + 2y = 9$$ 2. **Formula and method:** We can use the method of elimination or substitution to solve for $x$ and $y$. Here, we'll use elimination. 3. **Elimination step:** Multiply the first equation by 2 and the second equation by 5 to align coefficients of $y$: $$2(4x - 5y) = 2(-3) \Rightarrow 8x - 10y = -6$$ $$5(14x + 2y) = 5(9) \Rightarrow 70x + 10y = 45$$ 4. **Add the two equations:** $$8x - 10y + 70x + 10y = -6 + 45$$ $$78x = 39$$ 5. **Solve for $x$:** $$x = \frac{39}{78} = \frac{1}{2}$$ 6. **Substitute $x = \frac{1}{2}$ into the first original equation:** $$4\left(\frac{1}{2}\right) - 5y = -3$$ $$2 - 5y = -3$$ 7. **Solve for $y$:** $$-5y = -3 - 2 = -5$$ $$y = \frac{-5}{-5} = 1$$ **Final answer:** $$x = \frac{1}{2}, \quad y = 1$$