Question 481423
Let {{{ x }}} = number of brand x socks she bought
Let {{{ y }}} = number of brand y socks she bought
given:
(1) {{{ x + y = 16 }}}
(2) {{{ 15x + 20y = 260 }}}
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Multiply both sides of (1) by {{{ 15 }}}
and subtract (1) from (2)
(2) {{{ 15x + 20y = 260 }}}
(1) {{{ -15x - 15y = -240 }}}
{{{ 5y = 20 }}}
{{{ y = 4 }}}
and, since
(1) {{{ x + y = 16 }}}
(1) {{{ x + 4 = 16 }}}
(1) {{{ x = 12 }}} 
She bought 12 of brand x and 4 of brand y