1. **State the problem:** We are given three equations: $$2 + 3y + xb = 8 \quad (3)$$ $$1 = 2 + 3y + xb \quad (2)$$ $$x = 2 + 3y + xb \quad (1)$$ 2. **Analyze the equations:** Each equation expresses a relationship involving $x$, $y$, and $b$. Our goal is to understand or solve these equations. 3. **Rewrite each equation for clarity:** Equation (3): $$2 + 3y + xb = 8$$ Equation (2): $$1 = 2 + 3y + xb$$ Equation (1): $$x = 2 + 3y + xb$$ 4. **From equation (2), isolate $xb$:** $$1 = 2 + 3y + xb$$ Subtract $2 + 3y$ from both sides: $$1 - 2 - 3y = xb$$ $$\cancel{1} - \cancel{2} - 3y = xb$$ $$-1 - 3y = xb$$ 5. **Substitute $xb$ into equation (3):** $$2 + 3y + xb = 8$$ Replace $xb$ with $-1 - 3y$: $$2 + 3y + (-1 - 3y) = 8$$ Simplify: $$2 + 3y - 1 - 3y = 8$$ $$1 = 8$$ 6. **Check for consistency:** The statement $1 = 8$ is false, indicating the system is inconsistent. 7. **Conclusion:** The given system of equations has no solution because it leads to a contradiction.