1. **State the problem:** Solve the system of equations using substitution: $$3y = -4x - 1$$ $$3x - 2y = -22$$ 2. **Isolate one variable:** From the first equation, solve for $y$: $$3y = -4x - 1$$ $$y = \frac{-4x - 1}{3}$$ 3. **Substitute into the second equation:** Replace $y$ in the second equation with the expression found: $$3x - 2\left(\frac{-4x - 1}{3}\right) = -22$$ 4. **Simplify the equation:** $$3x - \frac{2(-4x - 1)}{3} = -22$$ Multiply both sides by 3 to clear the denominator: $$\cancel{3} \times 3x - \cancel{3} \times \frac{2(-4x - 1)}{\cancel{3}} = \cancel{3} \times -22$$ $$9x - 2(-4x - 1) = -66$$ 5. **Distribute and simplify:** $$9x + 8x + 2 = -66$$ $$17x + 2 = -66$$ 6. **Solve for $x$:** $$17x = -66 - 2$$ $$17x = -68$$ $$x = \frac{-68}{17}$$ $$x = -4$$ 7. **Find $y$ by substituting $x$ back:** $$y = \frac{-4(-4) - 1}{3} = \frac{16 - 1}{3} = \frac{15}{3} = 5$$ **Final answer:** $$x = -4, \quad y = 5$$