1. The problem involves solving the system of linear equations: $$\begin{cases} 7x - 8y = 45 \\ 8x - 7y = 88 \end{cases}$$ 2. We will use the substitution or elimination method to find $x$ and $y$. 3. From the second equation, isolate $x$ or $y$. For example, solve for $x$ in terms of $y$ or vice versa. 4. Alternatively, multiply the first equation by 8 and the second by 7 to align coefficients for elimination: $$\begin{cases} 56x - 64y = 360 \\ 56x - 49y = 616 \end{cases}$$ 5. Subtract the second from the first: $$ (56x - 64y) - (56x - 49y) = 360 - 616 $$ $$ -64y + 49y = -256 $$ $$ -15y = -256 $$ $$ y = \frac{256}{15} $$ 6. Substitute $y$ back into one of the original equations, for example, the first: $$ 7x - 8 \times \frac{256}{15} = 45 $$ $$ 7x = 45 + \frac{2048}{15} $$ $$ 7x = \frac{675}{15} + \frac{2048}{15} = \frac{2723}{15} $$ $$ x = \frac{2723}{105} $$ 7. The solution to the system is: $$ x = \frac{2723}{105}, \quad y = \frac{256}{15} $$ 8. The other equations and values given ($4x=114$, $x=3$, $9x-4y=45$, $y=24$) appear unrelated or inconsistent with the first system and are not used here. Final answer: $$ x = \frac{2723}{105}, \quad y = \frac{256}{15} $$