Question

Solve the equation by substitution or elemilation method

Answer 1

$\frac{2}{ \sqrt{x} } + \frac{3}{ \sqrt{y} } = 2 \\ \frac{4}{ \sqrt{x} } - \frac{9}{ \sqrt{y} } = - 1 \\ let \: \frac{1}{ \sqrt{x} } = a \: and \: \frac{1}{ \sqrt{y} } = b \\ = 2a + 3b = 2....................(1) \\ = 4a - 9b = - 1....................(2) \\ by \: elimination \: method \\ 2(2a + 3b = 2) \\ 4a - 9b = - 1 \\ = 4a + 6b = 4 \\ \: \: \: \: 4a - 9b = - 1 \\ (- ) \: \: \: (+ ) \: \: \: \: \: \: ( + )\\ ......................... \\ 15b = 5 \\ b = \frac{5}{15} \\ b = \frac{1}{3} \\ \\ putting \: value \: of \: b \: in \: eq(1) \\ 2a + 3( \frac{1}{3} ) = 2 \\ = 2a + 1 = 2 \\ a = \frac{1}{2} \\ a = \frac{1}{ \sqrt{x} } = \frac{1}{2} \\ = \sqrt{x} = 2 \\ x = {2}^{2} = 4 \\ b = \frac{1}{ \sqrt{y} } = \frac{1}{3} \\ = \sqrt{y} = 3 \\ y = {3}^{2} = 9$

HENCE SOLVED......

HOPE THIS HELPS MATE