Question 193782
Assuming  the  1st  eqn  is ...... 5y  +  2z  ....
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1)-6x+5y+2z = 10,,,,,mult  by  5....-30x+25y+10z=50
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2)-4x +5y +5z =29,,,,mult  by  2,,,,-8x +10y +10z =58
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3)-9x +4y +z =8,,,,,mult  by  10,,,,-90x +40y +10z = 80
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This  is  three  unknowns,,three  eqns,,,therefore  can  be  solved.
If  you  have  a  graphing  calculator,  and  know  augmented  matrix,  good  spot  to  use, otherwise,
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subtract  (2)  from  (1)  to  get,,,-22x+15y  =  -8,,,,,,,mult  by 2,,,-44x+30y+-16
substract  (2)  from(3)  to  get ,,,-82x+30y = 22
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subtract  again  to  get,,,-38x = 38,,,,x=(-1)ANSWER
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substitute ,,,-22(-1) +15y = -8
22+15y = -8
15y = -30,,,,y=(-2)  ANSWER
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substitute  in  original  (1),, -6(-1)+5(-2)+2z=10
6-10+2z = 10
2z = 14,,,,,,z=7  ANSWER
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check  by  subst  into  original  eqns
1) -6(-1)+5(-2)+2(7) = 10
6-10+14=10,,,,ok
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2) -4(-1)+5(-2)+5(7) = 29
4-10+35 = 29,,,,,ok
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3) -9(-1)+4(-2)+(7) =8
9-8+7 =8,,,,,,ok