Question 1058261
(1) {{{ x + y + z = 8 }}}
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(2) {{{ x - y/3 + (4/3)*z = 7 }}}
(2) {{{ 3x - y + 4z = 21 }}}
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(3) {{{ -2x - 3y + 3z = 7 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and add (1) and (3)
(1) {{{ 2x + 2y + 2z = 16 }}}
(3) {{{ -2x - 3y + 3z = 7 }}}
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{{{ -y + 5z = 23 }}}
Subtract (2) from this result
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{{{ -y + 5z = 23 }}}
(2) {{{ -3x + y - 4z = -21 }}}
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{{{ -3x + z = 2 }}}
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Now I can say:
{{{ y = 5z - 23 }}}
and
{{{ 3x = z - 2 }}}
{{{ x = (1/3)*z - 2/3 }}}
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Plug these results into (1)
(1) {{{ x + y + z = 8 }}}
(1) {{{ (1/3)*z - 2/3 + 5z - 23 + z = 8 }}}
(1) {{{ (19/3)*z = 31 + 2/3 }}} 
(1) {{{ 19z = 93 + 2 }}}
(1) {{{ z = 95/19 }}}
(1) {{{ z = 5 }}}
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{{{ -3x + z = 2 }}}
{{{ -3x + 5 = 2 }}}
{{{ -3x = -3 }}}
{{{ x = 1 }}}
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{{{ -y + 5z = 23 }}}
{{{ -y + 5*5 = 23 }}}
{{{ -y + 25 = 23 }}}
{{{ -y = -2 }}}
{{{ y = 2 }}}
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The solutions are:
x = 1
y = 2
z = 5
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check:
(1) {{{ x + y + z = 8 }}}
(1) {{{ 1 + 2 + 5 = 8 }}}
{1) {{{ 8 = 8 }}}
OK
You can check (2) and (3)