Question 1037104
Let {{{ a }}} = price of a chicken sandwich
Let {{{ b }}} = price of a cheese sandwich
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(1) {{{ 2a + 4b = 18 }}}
(2) {{{ 5a + 6b = 34 }}}
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Multiply both sides of (1) by {{{ 3 }}}
Multiply both sides of (2) by {{{ 2 }}}
Then subtract (1) from (2)
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(2) {{{ 10a + 12b = 68 }}}
(1) {{{ -6a - 12b = -54 }}}
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{{{ 4a = 14 }}}
{{{ a = 3.5 }}}
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Substitute this result into (1)
(1) {{{ 2a + 4b = 18 }}}
(1) {{{ 2*3.5 + 4b = 18 }}}
(1) {{{ 7 + 4b = 18 }}}
(1) {{{ 4b = 11 }}}
(1) {{{ b = 2.75 }}}
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The chicken sandwich is more expensive by 75 cents
{{{ 3.5 - 2.75 = .75 }}} 
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check:
(1) {{{ 2a + 4b = 18 }}}
(1) {{{ a + 2b = 9 }}}
(1) {{{ 3.5 + 2*2.75 = 9 }}}
(1) {{{ 3.5 + 5.5 = 9 }}}
(1) {{{ 9 = 9 }}}
OK
You can check (2)