1. **State the problem:** Solve the system of equations using substitution method: $$4x + 3y = -7$$ $$x = 6y + 5$$ 2. **Formula and rules:** Substitution method involves substituting the expression for one variable from one equation into the other equation. 3. **Substitute $x$ from the second equation into the first:** $$4(6y + 5) + 3y = -7$$ 4. **Expand and simplify:** $$24y + 20 + 3y = -7$$ $$27y + 20 = -7$$ 5. **Isolate $y$:** $$27y = -7 - 20$$ $$27y = -27$$ 6. **Divide both sides by 27:** $$y = \frac{\cancel{27}y}{\cancel{27}} = \frac{-27}{27}$$ $$y = -1$$ 7. **Substitute $y = -1$ back into $x = 6y + 5$ to find $x$:** $$x = 6(-1) + 5$$ $$x = -6 + 5$$ $$x = -1$$ **Final answer:** $$x = -1, y = -1$$