Answer: \((x, y) = (-1, 1)\)
Let \(5x + 2y = -3\) ... (I) and \(x + 5y = 4\) ... (II).
Multiply (I) by 5: \(25x + 10y = -15\)
Multiply (II) by 2: \(2x + 10y = 8\)
Subtract the equations to eliminate \(y\):\[23x = -23\]\[x = -1\]
Substitute \(x = -1\) in (I): \(2y = -3 - (-5) = 2\), so \(y = 1\).
Check in (II): \(1(-1) + 5(1) = 4\), which is true.