Question 1007667



Solve the system:
{{{ ( 2 / x ) + ( 3 / 2y ) = ( 11/4 ) }}}
{{{ (5 / 2x ) - ( 2 / y ) = ( 3 / 2 ) }}}
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I started by letting {{{ a = ( 1 / x ) }}} and {{{ b = ( 1 / y ) }}}.
So:
= {{{ ( 2a ) + ( 3 / 2 )b = ( 11/4 ) }}}
= {{{ (5 / 2 )a - ( 2b ) = ( 3 / 2 ) }}}
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Then I got rid of the denominators on the right side of the '=' through multiplication
So:
= {{{ ( 8a ) + ( 6b ) = ( 11 ) }}}
= {{{ (5a ) - ( 4b ) = ( 3 ) }}}
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Then I got rid of the denominators that were on the left side of the '='
So:
= {{{ ( 16a ) + ( 12b ) = ( 22 ) }}}
= {{{ (10a ) - ( 8b ) = ( 6 ) }}}
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Above, b does not cancel off by adding the two equations

you have to eliminate b

= {{{ ( 8a ) + ( 6b ) = ( 11 ) }}} * 2
= {{{ (5a ) - ( 4b ) = ( 3 ) }}}  ^ 3

we get

16a+12b = 22
15a -12b = 9
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add

31a = 31
a= 1

Plug a 

so we get b = 1/2

a= 1/x = 1 so x=1

b = 1/2 =`1/y

y=2

{{{ ( 2 / x ) + ( 3 / 2y ) = ( 11/4 ) }}}

{{{(2/1)+(3/4) }}}

{{{2+(3/4)}}}
 {{{11/4}}}