Question 264863
These are so much fun, Use substitution to solve
{{{300x+100y+50z=800}}} divide by 50 {{{6x+2y+z=16}}}
{{{20x+5y+5z=55}}} divide by 5 {{{4x+y+z=11}}}
{{{20y+44z=220}}} divide by 4 {{{5y+11z=55}}}
Re-write the reduced equations:
{{{6x+2y+z=16}}}
{{{4x+y+z=11}}}
{{{5y+11z=55}}} 
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{{{5y+11z=55}}} solve this one for "z"
{{{11z=55-5y}}}
{{{z=((55-5y)/11)}}}
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{{{4x+y+z=11}}} solve for y
{{{4x+y+((55-5y)/11)=11}}}
{{{44x+11y+(55-5y)=121}}}
{{{44x+6y+55=121}}}
{{{44x+6y=121-55}}}
{{{6y=66-44x}}}
{{{(6y)/6=((66-44x)/6)}}}
{{{y=((33-22x)/3)}}}
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{{{6x+2y+z=16}}} solve for x
{{{6x+2((33-22x)/3)+((55-5((33-22x)/3))/11)=16}}}
{{{(6x)(33)+22(33-22x)+(55)(3)-5(33-22x)=(16)(33)}}}
{{{198x+726-484x+165-165+110x=528}}}
{{{308x-484x=528-726}}}
{{{-176x=-198}}}
{{{x=((-198)/(-176))}}}
{{{x=(99/88)}}}
{{{x=9/8}}} x=9/8 now find "y" 
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{{{y=((33-22(9/8))/3)}}}
{{{3y(8)=33(8)-22(9))}}}
{{{24y=264-198}}}
{{{24y/24=66/24}}}
{{{y=66/24}}}
{{{y=11/4}}} y=11/4 now find "z"
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{{{z=((55-5y)/11)}}}
{{{z=((55-5(11/4))/11)}}}
{{{44z=(55(4)-5(11))}}}
{{{44z=(220-55)}}}
{{{44z/44=165/44}}}
{{{z=165/44}}}
{{{z=15/4}}} z=15/4 now to do a check
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{{{300(9/8)+100(11/4)+50(15/4)=800}}}
{{{300(9/8)+100(22/8)+50(30/8)=800}}}
{{{(2700/8)+(2200/8)+(1500/8)=800}}}
{{{((2700+2200+1500)/8)=800}}}
{{{(6400/8)=800}}}
{{{800=800}}} that means its correct
this took me a real long time I hope it will be easy to understand.