Question 715196
(1) {{{ x - 2y + 3z = 11 }}}
(2) {{{ 4x + 2y - 3z = 4 }}}
(3) {{{ 3x + 3y - z = 4 }}}
Add equations (1) and (2)
(1) {{{ x - 2y + 3z = 11 }}}
(2) {{{ 4x + 2y - 3z = 4 }}}
{{{ 5x = 15 }}}
{{{ x = 3 }}}
Plug this result into both (2) and (3)
(2) {{{ 4*3 + 2y - 3z = 4 }}}
(3) {{{ 3*3 + 3y - z = 4 }}}
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(2) {{{ 12 + 2y - 3z = 4 }}}
(3) {{{ 9 + 3y - z = 4 }}}
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(2) {{{ 2y - 3z = -8 }}}
(3) {{{ 3y - z = -5 }}}
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Multiply both sides of (3) by {{{ -3 }}}
and add (2) and (3)
(2) {{{ 2y - 3z = -8 }}}
(3) {{{ -9y + 3z = 15 }}}
{{{ -7y = 7 }}}
{{{ y = -1 }}}
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Plug this result into (2) or (3)
(2) {{{ 2y - 3z = -8 }}}
(2) {{{ 2*(-1) - 3z = -8 }}}
(2) {{{ -2 - 3z = -8 }}}
(2) {{{ -3z = -6 }}}
(2) {{{ z = 2 }}}
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{{{ x = 3 }}}
{{{ y = -1 }}}
{{{ z = 2 }}}