Explanation:
3x + y = 21 ... (i);
xy = 30 ... (ii)
From (ii), \(y = \frac{30}{x}\). Putting the value of y in (i), we have
3x + \(\frac{30}{x}\) = 21
\(\implies\) 3x\(^2\) + 30 = 21x
3x\(^2\) - 21x + 30 = 0
3x\(^2\) - 15x - 6x + 30 = 0
3x(x - 5) - 6(x - 5) = 0
(3x - 6)(x - 5) = 0
3x - 6 = 0 \(\implies\) x = 2.
x - 5 = 0 \(\implies\) x = 5.
If x = 2, y = \(\frac{30}{2}\) = 15;
If x = 5, y = \(\frac{30}{5}\) = 6.