1. The problem presents several equations involving variables with deltas ($\Delta t$, $\Delta x$, etc.) and algebraic expressions. We will analyze and simplify each equation where possible. 2. Equation (1): $81 = \Delta t + \Delta x$. This relates $\Delta t$ and $\Delta x$. 3. Equation (2): $6\Delta x = -1 \times \Delta x^2$ or $6\Delta x = -\Delta x^2$. Divide both sides by $\Delta x$ (assuming $\Delta x \neq 0$): $$6 = -\Delta x$$ So, $\Delta x = -6$. 4. Substitute $\Delta x = -6$ into equation (1): $$81 = \Delta t + (-6)$$ $$\Delta t = 81 + 6 = 87$$ 5. Equation (3) is unclear due to formatting: $080 = (5 + x) - 10202 \Delta 2$. Assuming $080$ means 80 and $\Delta 2$ is $\Delta^2$ or $\Delta_2$, but without clear definition, we cannot solve this. 6. Equation (4): $\Delta h4 + \frac{1}{\Delta 4h} + 54 \Delta x$ is incomplete (no equality). Cannot solve. 7. Equation (5): $2\Delta - \Delta^2 \Delta$ is incomplete (no equality). Cannot solve. 8. Equation: $5 = 4 + x \Delta \Delta$ is incomplete or unclear. 9. Equation: $0 = 1 + 54 - 269 1e$ is unclear and likely a typo. Summary: - From equations (1) and (2), we found $\Delta x = -6$ and $\Delta t = 87$. - Other equations are incomplete or unclear and cannot be solved without further clarification. Final answers: $$\boxed{\Delta x = -6, \quad \Delta t = 87}$$