1. **Stating the problem:** Solve the system of equations: First system: $$x = 5y - 2$$ $$4x - 9y = 36 + 4x$$ Second system: $$2y = x - 12$$ $$x - 2y = -1$$ 2. **Solve the first system:** From the first equation, we have: $$x = 5y - 2$$ Substitute this into the second equation: $$4(5y - 2) - 9y = 36 + 4(5y - 2)$$ Simplify both sides: $$20y - 8 - 9y = 36 + 20y - 8$$ Combine like terms: $$11y - 8 = 28 + 20y$$ Bring all terms to one side: $$11y - 8 - 28 - 20y = 0$$ Simplify: $$-9y - 36 = 0$$ Add 36 to both sides: $$-9y = 36$$ Divide both sides by -9: $$y = \frac{36}{\cancel{-9}}\cancel{-1} = -4$$ Substitute $y = -4$ back into $x = 5y - 2$: $$x = 5(-4) - 2 = -20 - 2 = -22$$ **Solution for first system:** $$x = -22, y = -4$$ 3. **Solve the second system:** Given: $$2y = x - 12$$ $$x - 2y = -1$$ Rewrite the first equation: $$x = 2y + 12$$ Substitute into the second equation: $$(2y + 12) - 2y = -1$$ Simplify: $$12 = -1$$ This is a contradiction, so the second system has **no solution**. **Final answers:** First system solution: $$x = -22, y = -4$$ Second system: No solution (inconsistent system).