Question

2x+3y+5=0,3x-2y-12 by elimination method
$\sqrt{x} + \sqrt{y} = 7 \\ \sqrt{x } - \sqrt{y } = 2$

Answer 1

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Answer 2

$2x + 3y = - 5 \: \: \: \: \: \: ......(1) \\ 3x - 2y = 12 \: \: \: \: \: \: .....(2) \\ multiply \: equcation \: (1) \: with \: 3 \: and \: equation \: (2) \: with \: (2) \: we \: get \\ 6x + 9y = - 15 \: \: \: \: \: ....(3) \\ 6x - 4y = 24 \: \: \: \: \: \: .....(4) \\ subtract \: equation \:( 4) \: from \: (3) \: we \: get \\ 13y = - 39 \\ y = - 3 \\ substitute \: the \: value \: of \: y = - 3 \: in \: equation \: (1) \\ 2x + 3( - 3) = - 5 \\ 2x - 9 = - 5 \\ 2x = - 5 + 9 \\ 2x = 4 \\ x= 2 \\ \\ \\ \\ \sqrt{x } + \sqrt{y} = 7 \: \: \: \: ....(1) \\ \sqrt{x} - \sqrt{y} = 2 \: \: \: \: ....(2) \\ add \: equation \: (1) and \: (2) \: we \: get \\ 2 \sqrt{x} = 9 \\ \sqrt{x} = \frac{9}{2} \\ squaring \: on \: both \: sides \\ x = \frac{81}{4} \\ substitute \: the \: value \: of \: x= \frac{81}{4} \: in \: equation \: (1) \\ \sqrt{ \frac{81}{4} } + \sqrt{y} = 7 \\ \frac{9}{2} + \sqrt{y} = 7 \\ \sqrt{y} = 7 - \frac{9}{2} \\ \sqrt{y} = \frac{14 - 9}{2} \\ \sqrt{y} = \frac{5}{2} \\ squaring \: on \: both \: sides \\ y = \frac{25}{4}$