1. **State the problem:** Solve the system of linear equations: $$-2x = y$$ $$4x + 10y = 16$$ 2. **Use substitution method:** From the first equation, express $y$ in terms of $x$: $$y = -2x$$ 3. **Substitute $y$ into the second equation:** $$4x + 10(-2x) = 16$$ 4. **Simplify the equation:** $$4x - 20x = 16$$ $$\cancel{4x} - 20x = 16$$ $$-16x = 16$$ 5. **Solve for $x$:** $$x = \frac{16}{-16} = -1$$ 6. **Find $y$ using $y = -2x$:** $$y = -2(-1) = 2$$ 7. **Final answer:** $$x = -1, \quad y = 2$$ This means the solution to the system is the point $(-1, 2)$ where both lines intersect.