Question 664543
(1) {{{ 1/(2x) + 3/(2y) = 3/8 }}} 
(2) {{{ 9/x - 6/y = 15/12 }}}
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Are these the right equations?
If so, 
Multiply both sides of (1) by {{{ 8x*y }}}
(1) {{{ 4y + 12x = 3x*y }}}
Multiply both sides of (2) by {{{ 12x*y }}}
(2) {{{ 108y - 72x = 15x*y }}}
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Multiply both sides of (1) by {{{ 6 }}}
and add the equations
(1) {{{ 24y + 72x = 18x*y }}}
(2) {{{ 108y - 72x = 15x*y }}}
{{{ 132y = 33x*y }}}
Divide both sides by {{{ y }}}
{{{ x = 132/33 }}}
{{{ x = 44/11 }}}
{{{ x = 4 }}}
Now plug this back into (1) or (2)
(1) {{{ 4y + 12x = 3x*y }}}
(1) {{{ 4y + 12*4 = 3*4*y }}}
(1) {{{ 4y + 48 = 12y }}}
(1) {{{ 8y = 48 }}}
(1) {{{ y = 6 }}}
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check solutions:
(1) {{{ 1/(2x) + 3/(2y) = 3/8 }}} 
(1) {{{ 1/(2*4) + 3/(2*6) = 3/8 }}} 
(1) {{{ 1/8 + 1/4 = 3/8 }}}
(1) {{{ 3/8 = 3/8 }}}
OK
and
(2) {{{ 9/x - 6/y = 15/12 }}}
(2) {{{ 9/4 - 6/6 = 15/12 }}}
(2) {{{ 27/12 - 12/12 = 15/12 }}}
(2) {{{ 27 - 12 = 15 }}}
(2) {{{ 15 = 15 }}}
OK