1. **State the problem:** Solve the system of linear equations: $$-2x + 3y = 14$$ $$x + 2y = 7$$ 2. **Choose a method:** We will use substitution or elimination. Here, substitution is straightforward. 3. **Express $x$ from the second equation:** $$x + 2y = 7 \implies x = 7 - 2y$$ 4. **Substitute $x$ into the first equation:** $$-2(7 - 2y) + 3y = 14$$ 5. **Simplify:** $$-14 + 4y + 3y = 14$$ $$7y - 14 = 14$$ 6. **Isolate $y$:** $$7y = 14 + 14$$ $$7y = 28$$ $$y = \frac{28}{7}$$ $$y = 4$$ 7. **Substitute $y=4$ back into $x = 7 - 2y$:** $$x = 7 - 2(4)$$ $$x = 7 - 8$$ $$x = -1$$ 8. **Final answer:** $$x = -1, \quad y = 4$$