Question

2/√x+3/√y=2
4/√x-9/√y=-1​

Answer 1

Let 1/√x = a and

1/√y = b

$\frac{2}{ \sqrt{x} } + \frac{3}{ \sqrt{y} } = 2 \\ 2a + 3b = 2 - - - (1)\\ \\ \frac{4}{ \sqrt{x} } - \frac{9}{ \sqrt{y} } = - 1 \\ 4a - 9b = - 1 - - - (2) \\ \\ (1) \times 3 \\ 6a + 9b = 6 - - - (3) \\ \\ (2) + (3) \\ 4a - 9b + 6a + 9b = - 1 + 6 \\ 10a = - 5 \\ a = \frac{ -1 }{2} \\ \\ substitute \: this \: in \: (1) \\ 2 \times \frac{ - 1}{2} + 3b = 2 \\ 3b - 1 = 2 \\ 3b = 3 \\ b = 1$

$\frac{1}{ \sqrt{x} } = a = \frac{ - 1}{2} \\ \sqrt{x} = - 2 \\ x = {( -2 )}^{2} = 4 \\ \\ \frac{1}{ \sqrt{y} } = b = 1 \\ \sqrt{y} = 1 \\ y = 1$

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