1. **State the problem:** Solve the system of equations: $$-3x - 2y = -4$$ $$9x + 3y = 15$$ 2. **Choose a method:** We will use the elimination method to solve for $x$ and $y$. 3. **Make coefficients of $y$ equal:** Multiply the first equation by 3 to align the $y$ coefficients: $$3 \times (-3x - 2y) = 3 \times (-4)$$ $$-9x - 6y = -12$$ 4. **Write the new system:** $$-9x - 6y = -12$$ $$9x + 3y = 15$$ 5. **Add the two equations to eliminate $x$:** $$(-9x - 6y) + (9x + 3y) = -12 + 15$$ $$-9x + 9x - 6y + 3y = 3$$ $$-3y = 3$$ 6. **Solve for $y$:** $$y = \frac{3}{-3}$$ $$y = -1$$ 7. **Substitute $y = -1$ into the first original equation:** $$-3x - 2(-1) = -4$$ $$-3x + 2 = -4$$ 8. **Solve for $x$:** $$-3x = -4 - 2$$ $$-3x = -6$$ $$x = \frac{-6}{-3}$$ $$x = 2$$ **Final answer:** $$x = 2, \quad y = -1$$