Answer: \((x, y) = (2, -1)\)
In the form \(a_1x + b_1y = c_1\), \(a_2x + b_2y = c_2\):\[3x - 4y = 10\]\[4x + 3y = 5\]
\(D = \begin{vmatrix} 3 & -4 \\ 4 & 3 \end{vmatrix}\)\[D = 3\times 3 - (-4)\times 4 = 25\]
\(D_x = \begin{vmatrix} 10 & -4 \\ 5 & 3 \end{vmatrix}\)\[D_x = 10\times 3 - (-4)\times 5 = 50\]
\(D_y = \begin{vmatrix} 3 & 10 \\ 4 & 5 \end{vmatrix}\)\[D_y = 3\times 5 - 10\times 4 = -25\]
By Cramer's rule:\[x = \frac{D_x}{D} = \frac{50}{25} = 2\]\[y = \frac{D_y}{D} = \frac{-25}{25} = -1\]