1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x = -5y \\ 3y + 2x = -21 \end{cases}$$ 2. **Use substitution:** Since $x = -5y$, substitute $x$ in the second equation: $$3y + 2(-5y) = -21$$ 3. **Simplify the equation:** $$3y - 10y = -21$$ $$-7y = -21$$ 4. **Solve for $y$:** $$y = \frac{-21}{-7}$$ $$y = \cancel{\frac{-21}{-7}} 3$$ 5. **Find $x$ using $x = -5y$:** $$x = -5(3)$$ $$x = -15$$ 6. **Write the solution as an ordered pair:** $$(x, y) = (-15, 3)$$ This is the solution to the system of equations by substitution.