Question 883915
Let {{{ a }}} = the weight in kg of a large box
Let {{{ b }}} = the weight in kg of a small box
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(1) {{{ 5a + 2b = 103 }}}
(2) {{{ 3a + 8b = 106 }}}
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Multiply both sides of (1) by {{{ 4 }}}
and subtract (2) from (1)
(1) {{{ 20a + 8b = 412 }}}
(2) {{{ -3a - 8b = -106 }}}
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{{{ 17a = 306 }}}
{{{ a = 18 }}}
and
(1) {{{ 5*18 + 2b = 103 }}}
(1) {{{ 90 + 2b = 103 }}}
(1) {{{ 2b = 13 }}}
(1) {{{ b = 6.5 }}}
The large box weighs 18 kg and
the small box weighs 6.5 kg
check:
(2) {{{ 3a + 8b = 106 }}}
(2) {{{ 3*18 + 8*6.5 = 106 }}}
(2) {{{ 54 + 52 = 106 }}}
(2) {{{ 106 = 106 }}}
OK