Answer: \((x, y) = (7, 3)\)
\(49x - 57y = 172\) ... (I) and \(57x - 49y = 252\) ... (II).
Adding (I) and (II):\[106x - 106y = 424\]\[x - y = 4 \quad \text{(III)}\]
Subtracting (I) from (II):\[8x + 8y = 80\]\[x + y = 10 \quad \text{(IV)}\]
Adding (III) and (IV): \(2x = 14\), so \(x = 7\). Then from (IV), \(y = 10 - 7 = 3\).
Check in (I): \(49(7) - 57(3) = 343 - 171 = 172\), which is true.