1. **State the problem:** Solve the system of equations using substitution: $$\begin{cases} 3x + 4y = 7 \\ y = 2x + 10 \end{cases}$$ 2. **Use substitution:** Since the second equation gives $y$ in terms of $x$, substitute $y = 2x + 10$ into the first equation. 3. **Substitute and simplify:** $$3x + 4(2x + 10) = 7$$ $$3x + 8x + 40 = 7$$ $$11x + 40 = 7$$ 4. **Isolate $x$:** $$11x = 7 - 40$$ $$11x = -33$$ 5. **Divide both sides by 11:** $$x = \frac{-33}{11}$$ $$x = \cancel{\frac{-33}{11}} = -3$$ 6. **Find $y$ by substituting $x = -3$ into $y = 2x + 10$:** $$y = 2(-3) + 10$$ $$y = -6 + 10$$ $$y = 4$$ **Final answer:** $$x = -3, \quad y = 4$$