SOLUTION: Solve using REF x-y-2z=0 -2x+5y+10z=-3 3x+y=0

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Question 126485: Solve using REF
x-y-2z=0
-2x+5y+10z=-3
3x+y=0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x-y-2z=0………………………………(1)
-2x%2B5y%2B10z=-3……………………….(2)
3x%2By=0………………………………..(3)

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x-y-2z=0………………………………(1)…=>
x+=+y+%2B+2z………………plug into (2)

-2%28y+%2B+2z+%29+%2B+5y+%2B+10z+=+-3 ……………………….(2)

-2y+-+4z++%2B+5y+%2B+10z+=+-3
3y+%2B+6z+=+-3………………………(I)
Now plug x into (3)
3%28y+%2B+2z+%29%2By=0 ………………………………..(3)
3y+%2B+6z+%2By=0
4y+%2B+6z+=0…………………………..(II)
subtract (II) from (I) to solve for y

3y+%2B+6z+=+-3………………………(I)
4y+%2B+6z+=0…………………………..(II)
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3y-4y%2B6z-6z=+-3+%96+0
-y%2Bcross%286z%29-cross%286z%29+=+-3+
highlight%28y+=+3%29+
3x%2By=0 ………………………………..(3)…plug in y and find x
3x%2B3=0
3x+=+-3
highlight%28x+=+-1%29

x-y-2z=0 ………………………………(1)….. plug in x and y, then find z
-1-3-2z=0
-4-2z=0
-4+=+2z
-4%2F2+=+z
highlight%28z+=+-2%29+

Check:

x-y-2z=0 ………………………………(1)
-1-3-2%28-2%29+=+0
-4+%2B+4+=+0
0+=+0

-2x%2B5y%2B10z=-3 ……………………….(2)
-2%28-1%29%2B5%2A3%2B10%28-2%29+=-3

2+%2B+15++-20+=+-3
+17++-20+=+-3
+-3++=+-3

3x%2By=0 ………………………………..(3)
3%28-1%29+%2B+3+=+0
-3+%2B+3+=+0
0+=+0