1. **State the problem:** Solve the simultaneous equations: $$-x + 4y = 9$$ $$2x + 2y + 3 = 0$$ 2. **Rewrite the second equation:** $$2x + 2y = -3$$ 3. **Express one variable from the first equation:** From $$-x + 4y = 9$$, add $$x$$ to both sides: $$4y = x + 9$$ Then subtract 9: $$4y - 9 = x$$ 4. **Substitute $$x$$ into the second equation:** $$2(4y - 9) + 2y = -3$$ 5. **Expand and simplify:** $$8y - 18 + 2y = -3$$ Combine like terms: $$10y - 18 = -3$$ 6. **Add 18 to both sides:** $$10y = -3 + 18$$ $$10y = 15$$ 7. **Divide both sides by 10:** $$y = \frac{\cancel{10}y}{\cancel{10}} = \frac{15}{10} = \frac{3}{2}$$ 8. **Substitute $$y = \frac{3}{2}$$ back into $$x = 4y - 9$$:** $$x = 4 \times \frac{3}{2} - 9 = 6 - 9 = -3$$ **Final answer:** $$x = -3, \quad y = \frac{3}{2}$$