SOLUTION: 1/3x - 1/4y + z = -9 1/2x - 1/3y - 1/4z = -6 x - 1/2y - z = -8 I tried multiplying the 1st two by 12 and third by 2 and also tried all three by 12, I think I am mis

Algebra ->  Linear-equations -> SOLUTION: 1/3x - 1/4y + z = -9 1/2x - 1/3y - 1/4z = -6 x - 1/2y - z = -8 I tried multiplying the 1st two by 12 and third by 2 and also tried all three by 12, I think I am mis      Log On


   

Question 767482: 1/3x - 1/4y + z = -9
1/2x - 1/3y - 1/4z = -6
x - 1/2y - z = -8

I tried multiplying the 1st two by 12 and third by 2 and also tried all three by 12, I think I am missing something when I try to solve it.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%281%2F3%29x+-+%281%2F4%29y+%2B+z+=+-9.........eq.1.....multiply by 12
%281%2F2%29x+-+%281%2F3%29y+-+%281%2F4%29z+=+-6....eq.2....multiply by 12
x+-+%281%2F2%29y+-+z+=+-8..............eq.3....multiply by 2
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12%281%2F3%29x+-+12%281%2F4%29y+%2B+12z+=+-9%2A12.........eq.1
12%281%2F2%29x+-+12%281%2F3%29y+-+12%281%2F4%29z+=+-6%2A12....eq.2
2x+-+2%281%2F2%29y+-+2z+=+-8%2A2..............eq.3
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4x+-+3y+%2B+12z+=+-108.........eq.1
6x+-+4y+-+3z+=+-72....eq.2
2x+-+y+-+2z+=+-16..............eq.3
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6x+-+4y+-+3z+=+-72....eq.2
2x+-+y+-+2z+=+-16..............eq.3....multiply by 3
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6x+-+4y+-+3z+=+-72....eq.2
6x+-+3y+-+6z+=+-48..............eq.3......subtract eq.3 from eq.2
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6x-6x+-+4y-%28-3y%29+-+3z-%28-6z%29+=+-72-%28-48%29
-+4y%2B3y+-+3z%2B6z+=+-72%2B48
-y%2B3z+=+-24.....solve for y
24%2B3z+=+y.....plug in eq.1

4x+-+3%2824%2B3z%29+%2B+12z+=+-108.........eq.1
4x+-+72-9z+%2B+12z+=+-108
4x++%2B+3z+=+-108%2B72
4x++%2B+3z+=+-36......solve for x
+4x=+-3z-36
+x+=+-%283%2F4%29z-9.........go to eq.3 and plug in y and x
2x+-+y+-+2z+=+-16..............eq.3.
2%28-%283%2F4%29z-9%29+-+%2824%2B3z+%29-+2z+=+-16 ....solve for z
-%283%2F2%29z-18+-+24-3z+-+2z+=+-16...all terms multiply by 2
-2%283%2F2%29z-18%2A2+-+24%2A2-5%2A2z+=+-16%2A2
-3z-36-+48-10z+=+-32
32-36-+48+=+3z%2B10z
32-84+=13z
-52+=13z
-52%2F13=z
highlight%28z=-4%29..........now we can find x and y

+x+=+-%283%2F4%29z-9=>+x+=+-%283%2F4%29%28-4%29-9 =>+x+=+3-9=>+highlight%28x+=+-6%29
y=24%2B3z+=>y=24%2B3%28-4%29+=>y=24-12+=>highlight%28y=12%29+