Question 1081639
(1) {{{ x + y = 8 }}}
(2) {{{ .5x + .3y = 2.8 }}}
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(2) {{{ 5x + 3y = 28 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 5x + 3y = 28 }}}
(1) {{{ -3x - 3y = -24 }}}
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{{{ 2x = 4 }}}
{{{ x = 2 }}}
and
(1) {{{ 2 + y = 8 }}}
(1) {{{ y = 6 }}}
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2 gallons of the 50% solution are needed
6 gallons of the 30% solution are needed
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check:
(2) {{{ .5x + .3y = 2.8 }}}
(2) {{{ .5*2 + .3*6 = 2.8 }}}
(2) {{{ 1 + 1.8 = 2.8 }}}
(2) {{{ 2.8 = 2.8 }}}
OK