Question 1127836


Solve the of equation 
{{{2x-y+z=-7}}}................eq.1
{{{ x-3y+4z=-19}}}...........eq.2
{{{-x+4y-3z=18}}}...........eq.3
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start with
{{{ x-3y+4z=-19}}}...........eq.2
{{{-x+4y-3z=18}}}...........eq.3..........add both
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{{{ x-3y+4z-x+4y-3z=-19+18}}}

{{{ z+y=-1}}}
{{{ z=-1-y}}}..........(1a)


{{{2x-y+z=-7}}}................eq.1
{{{ x-3y+4z=-19}}}...........eq.2........multiply by {{{2}}} 
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{{{2x-y+z=-7}}}................eq.1. 
{{{ 2x-6y+8z=-38}}}...........eq.2............subtract
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{{{2x-y+z-(2x-6y+8z)=-7-(-38)}}}
{{{2x-y+z-2x+6y-8z=-7+38}}}
{{{5y-7z=31}}}
{{{5y-31=7z}}}
{{{z=(5y-31)/7}}}..........(1b)

from (1a) and (1b) we have

{{{(5y-31)/7=-1-y}}}
{{{5y-31=-7-7y}}}
{{{5y+7y=31-7}}}
{{{12y=24}}}
{{{highlight(y=2)}}}

go to {{{ z=-1-y}}}..........(1a), plug in {{{y}}} value

{{{ z=-1-2}}}
{{{ highlight(z=-3)}}}

go to {{{2x-y+z=-7}}}................eq.1 plug in {{{y}}} and {{{z}}} value

{{{2x-2-3=-7}}}
{{{2x-5=-7}}}
{{{2x=-7+5}}}
{{{2x=-2}}}
{{{highlight(x=-1)}}}


answer: A. There is one solution ({{{-1}}},{{{2}}},{{{-3}}})