1. **State the problem:** We are given the system of equations: $$\begin{cases} 3x_1 + 4x_2 + s_1 = 14 \\ x_1 + 5x_2 + s_2 = 7 \end{cases}$$ with the conditions $x_2 = 0$ and $s_2 = 0$. We need to find the solution $(x_1, x_2, s_1, s_2)$. 2. **Substitute the given values:** Since $x_2 = 0$ and $s_2 = 0$, substitute these into the system: $$\begin{cases} 3x_1 + 4 \times 0 + s_1 = 14 \\ x_1 + 5 \times 0 + 0 = 7 \end{cases}$$ which simplifies to: $$\begin{cases} 3x_1 + s_1 = 14 \\ x_1 = 7 \end{cases}$$ 3. **Solve for $x_1$:** From the second equation, we have: $$x_1 = 7$$ 4. **Find $s_1$ using the first equation:** Substitute $x_1 = 7$ into the first equation: $$3 \times 7 + s_1 = 14$$ $$21 + s_1 = 14$$ 5. **Isolate $s_1$:** $$s_1 = 14 - 21$$ $$s_1 = -7$$ 6. **Write the solution:** The solution is: $$(x_1, x_2, s_1, s_2) = (7, 0, -7, 0)$$ This matches the given basic solution. **Final answer:** $$(7, 0, -7, 0)$$