1. **State the problem:** Solve the system of equations: $$\begin{cases} -x - 5z = -5 \\ y - 3x = 0 \\ 13x + 2z = 2 \end{cases}$$ 2. **Express $y$ in terms of $x$ from the second equation:** $$y - 3x = 0 \implies y = 3x$$ 3. **Use the first and third equations to solve for $x$ and $z$:** From the first equation: $$-x - 5z = -5 \implies -x = -5 + 5z \implies x = 5 - 5z$$ Substitute $x = 5 - 5z$ into the third equation: $$13x + 2z = 2$$ $$13(5 - 5z) + 2z = 2$$ $$65 - 65z + 2z = 2$$ $$65 - 63z = 2$$ 4. **Solve for $z$:** $$-63z = 2 - 65$$ $$-63z = -63$$ $$z = \frac{-63}{-63} = 1$$ 5. **Find $x$ using $z=1$:** $$x = 5 - 5(1) = 5 - 5 = 0$$ 6. **Find $y$ using $x=0$:** $$y = 3(0) = 0$$ 7. **Final solution:** $$(x, y, z) = (0, 0, 1)$$ This matches option A.