\(3x + y = 8 ... (i)\) \(x^{2} + xy = 6 ... (ii)\) From (i), \(y = 8 - 3x\) From (ii), \(xy = 6 - x^{2} \implies y = \frac{6 - x^{2}}{x}\) Equating the two values of y, we have \(8 - 3x = \frac{6 - x^{2}}{x} \implies x(8 - 3x) = 6 - x^{2}\) \(8x - 3x^{2} = 6 - x^{2} \implies 6 - x^{2} - 8x + 3x^{2} = 0\) \(2x^{2} - 8x + 6 = 0\) \(x^{2} - 4x + 3 = 0\) \(x^{2} - 3x - x + 3 = 0 \implies x(x - 3) - 1(x - 3) = 0\) \((x - 1)(x - 3) = 0 \therefore \text{x = 1 or 3}\) \(y = 8 - 3x \) When x = 1, \(y = 8 - 3(1) = 5\) When x = 3, \(y = 8 - 3(3) = -1\) \(\therefore \text{y = -1 or 5}\)