Question 1079336
(1) {{{ (2/x^2)+(3/y^2)=(5/6)) }}}
(2) {{{ (4/x^2)-(9/y^2)=0) }}}
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Multiply both sides of (1) by {{{ 3 }}}
and add the equations
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(1) {{{ (6/x^2)+(9/y^2)=(5/2)) }}}
(2) {{{ (4/x^2)-(9/y^2)=0) }}}
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{{{ 10/x^2 = 5/2 }}}
{{{ 10/x^2 = 10/4 }}}
{{{ x^2 = 4 }}}
{{{ x = 2 }}}
{{{ x = -2 }}}
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Plug this result back into (1) or (2)
(2) {{{ (4/x^2)-(9/y^2)=0) }}}
(2) {{{ (4/4)-(9/y^2)=0) }}}
(2) {{{ 1 - 9/y^2 = 0 }}}
(2) {{{ 9/y^2 = 1 }}}
(2) {{{ 9/y^2 = 9/9 }}}
(2) {{{ y^2 = 9 }}}
(2) {{{ y = 3 }}}
(2) {{{ y = -3 }}}
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I believe the solutions are:
( 2,3 ), ( 2.-3 ) and
( -2,3 ), ( -2,-3 )