Question 801198
Let {{{ a }}} = number of 1 pound bags
Let {{{ b }}} = number of 3 pound bags
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(1) {{{ a + b = 5 }}}
(2) {{{ 2a + 5.5b = 17 }}}
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Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a + 5.5b = 17 }}}
(1) {{{ -2a - 2b = -10 }}}
{{{ 3.5b = 7 }}}
{{{ b = 2 }}}
and, since
(1) {{{ a + b = 5 }}}
(1) {{{ a = 3 }}}
You bought 3 1-pound bags and 
2 3-pound bags
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check:
(2) {{{ 2a + 5.5b = 17 }}}
(2) {{{ 2*3 + 5.5*2 = 17 }}} 
(2) {{{ 6 + 11 = 17 }}}
(2) {{{ 17 = 17 }}}
OK