Question 1152659


{{{6x+z=21}}}.............1)
{{{4x+6y=34}}}.............2)
{{{-5y+6z=-33}}}.............3)
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{{{6x+z=21}}}.............1)........solve for {{{z}}}

{{{z=-6x+21}}}........1a)

{{{-5y+6z=-33}}}.............3)......solve for {{{z}}}

{{{z=5y/6-33/6}}}

{{{z=5y/6-11/2}}}........2a)


from 1a) and 2a) we have

{{{-6x+21=5y/6-11/2}}}.....solve for {{{x}}}

{{{-6x=5y/6-33/6-21}}}

{{{-6x=(5 y)/6 - 53/2}}}

{{{x=(5 y)/-36 - 53/-12}}}

{{{x= 53/12 - (5 y)/36}}}........3a)


go to

{{{z=-6x+21}}}........1a), substitute {{{x}}}

{{{z=-6(53/12 - (5 y)/36)+21}}}

{{{z=  (5 y)/6 - 11/2}}}

go to

{{{4x+6y=34}}}.............3),  substitute {{{x}}}

{{{4(53/12 - (5 y)/36)+6y=34}}}.........solve for {{{y}}}

{{{(49 y)/9 + 53/3 =34}}}


{{{(49 y)/9  = 34- 53/3}}}
{{{(49 y)/9  = 102/3- 53/3}}}

{{{(49 y)/9  = 49/3}}}

{{{(49 y)  = 9(49/3)}}}

{{{(49 y)  = 3(49)}}}

{{{y = 3(49/49 )}}}

{{{y = 3}}}

go to
{{{z=5y/6-11/2}}}........2a), substitute {{{y}}}

{{{z=(5*3)/6-11/2}}}

{{{z=5/2-11/2}}}

{{{z=-6/2}}}

{{{z=-3}}}


go to

{{{z=-6x+21}}}........1a), substitute {{{z}}}


{{{-3=-6x+21}}}.......solve for {{{x}}}

{{{6x=3+21}}}

{{{6x=24}}}

{{{x=4}}}

solutions:

{{{x = 4}}}, {{{y = 3}}}, {{{z = -3}}}