1. **State the problem:** Solve the system of equations: $$\begin{cases} x + y + z = w \\ -x - 2y - 3z = -24 \\ -x + 5y = ? \end{cases}$$ Note: The third equation is incomplete; assuming it is $-x + 5y = 0$ to proceed. 2. **Write the system clearly:** $$\begin{cases} x + y + z = w \\ -x - 2y - 3z = -24 \\ -x + 5y = 0 \end{cases}$$ 3. **Express $x$ from the third equation:** $$-x + 5y = 0 \implies x = 5y$$ 4. **Substitute $x=5y$ into the first and second equations:** First equation: $$5y + y + z = w \implies 6y + z = w$$ Second equation: $$-5y - 2y - 3z = -24 \implies -7y - 3z = -24$$ 5. **Solve the system for $y$ and $z$:** From the first: $$z = w - 6y$$ Substitute into the second: $$-7y - 3(w - 6y) = -24$$ Simplify: $$-7y - 3w + 18y = -24$$ $$11y - 3w = -24$$ 6. **Solve for $y$:** $$11y = 3w - 24$$ $$y = \frac{3w - 24}{11}$$ 7. **Find $z$:** $$z = w - 6 \times \frac{3w - 24}{11} = w - \frac{18w - 144}{11} = \frac{11w - 18w + 144}{11} = \frac{-7w + 144}{11}$$ 8. **Find $x$:** $$x = 5y = 5 \times \frac{3w - 24}{11} = \frac{15w - 120}{11}$$ **Final solution:** $$x = \frac{15w - 120}{11}, \quad y = \frac{3w - 24}{11}, \quad z = \frac{-7w + 144}{11}$$