SOLUTION: 300x+100y+50z=800 20x+5y+5z=55 20y+44z=220

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Question 264863: 300x+100y+50z=800
20x+5y+5z=55
20y+44z=220
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
These are so much fun, Use substitution to solve
300x%2B100y%2B50z=800 divide by 50 6x%2B2y%2Bz=16
20x%2B5y%2B5z=55 divide by 5 4x%2By%2Bz=11
20y%2B44z=220 divide by 4 5y%2B11z=55
Re-write the reduced equations:
6x%2B2y%2Bz=16
4x%2By%2Bz=11
5y%2B11z=55
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5y%2B11z=55 solve this one for "z"
11z=55-5y
z=%28%2855-5y%29%2F11%29
.
4x%2By%2Bz=11 solve for y
4x%2By%2B%28%2855-5y%29%2F11%29=11
44x%2B11y%2B%2855-5y%29=121
44x%2B6y%2B55=121
44x%2B6y=121-55
6y=66-44x
%286y%29%2F6=%28%2866-44x%29%2F6%29
y=%28%2833-22x%29%2F3%29
.
6x%2B2y%2Bz=16 solve for x
6x%2B2%28%2833-22x%29%2F3%29%2B%28%2855-5%28%2833-22x%29%2F3%29%29%2F11%29=16
%286x%29%2833%29%2B22%2833-22x%29%2B%2855%29%283%29-5%2833-22x%29=%2816%29%2833%29
198x%2B726-484x%2B165-165%2B110x=528
308x-484x=528-726
-176x=-198
x=%28%28-198%29%2F%28-176%29%29
x=%2899%2F88%29
x=9%2F8 x=9/8 now find "y"
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y=%28%2833-22%289%2F8%29%29%2F3%29
3y%288%29=33%288%29-22%289%29%29
24y=264-198
24y%2F24=66%2F24
y=66%2F24
y=11%2F4 y=11/4 now find "z"
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z=%28%2855-5y%29%2F11%29
z=%28%2855-5%2811%2F4%29%29%2F11%29
44z=%2855%284%29-5%2811%29%29
44z=%28220-55%29
44z%2F44=165%2F44
z=165%2F44
z=15%2F4 z=15/4 now to do a check
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300%289%2F8%29%2B100%2811%2F4%29%2B50%2815%2F4%29=800
300%289%2F8%29%2B100%2822%2F8%29%2B50%2830%2F8%29=800
%282700%2F8%29%2B%282200%2F8%29%2B%281500%2F8%29=800
%28%282700%2B2200%2B1500%29%2F8%29=800
%286400%2F8%29=800
800=800 that means its correct
this took me a real long time I hope it will be easy to understand.