Answer: \((x, y) = (3, 1)\)
Let \(x + 7y = 10\) ... (I) and \(3x - 2y = 7\) ... (II).
Multiply (I) by 2: \(2x + 14y = 20\)
Multiply (II) by 7: \(21x - 14y = 49\)
Add the equations to eliminate \(y\):\[23x = 69\]\[x = 3\]
Substitute \(x = 3\) in (I): \(7y = 10 - 3 = 7\), so \(y = 1\).
Check in (II): \(3(3) + (-2)(1) = 7\), which is true.