1. **State the problem:** We are given the system of equations: $$4x_1 + 5x_2 + s_1 = 15$$ $$x_1 + 3x_2 + s_2 = 16$$ and asked to find the solution when $x_1 = 0$ and $s_1 = 0$. 2. **Substitute the given values:** Substitute $x_1 = 0$ and $s_1 = 0$ into the first equation: $$4(0) + 5x_2 + 0 = 15$$ which simplifies to: $$5x_2 = 15$$ 3. **Solve for $x_2$:** Divide both sides by 5: $$\cancel{5}x_2 = \cancel{5}3$$ $$x_2 = 3$$ 4. **Find $s_2$ using the second equation:** Substitute $x_1 = 0$ and $x_2 = 3$ into the second equation: $$0 + 3(3) + s_2 = 16$$ Simplify: $$9 + s_2 = 16$$ 5. **Solve for $s_2$:** Subtract 9 from both sides: $$s_2 = 16 - 9$$ $$s_2 = 7$$ 6. **Write the basic solution:** The solution is: $$(x_1, x_2, s_1, s_2) = (0, 3, 0, 7)$$ This matches the given basic solution, confirming the correctness.