1. **State the problem:** Solve the system of linear equations: $$3x - 4y = 7$$ $$2x + y = -10$$ 2. **Formula and method:** We can use substitution or elimination. Here, we'll use substitution. 3. **Isolate $y$ in the second equation:** $$2x + y = -10 \implies y = -10 - 2x$$ 4. **Substitute $y$ into the first equation:** $$3x - 4(-10 - 2x) = 7$$ 5. **Simplify:** $$3x + 40 + 8x = 7$$ $$11x + 40 = 7$$ 6. **Solve for $x$:** $$11x = 7 - 40$$ $$11x = -33$$ $$x = \frac{-33}{11} = -3$$ 7. **Substitute $x = -3$ back into $y = -10 - 2x$:** $$y = -10 - 2(-3) = -10 + 6 = -4$$ 8. **Final answer:** $$x = -3, \quad y = -4$$