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Find Elimination x+y+z=9,2x+y-z=0,2x+5y+7z=52

Solution:
Your problem -> Elimination x+y+z=9,2x+y-z=0,2x+5y+7z=52

Total Equations are 3

x+y+z=9 -> (1)

2x+y-z=0 -> (2)

2x+5y+7z=52 -> (3)

Select the equations (1) and (2), and eliminate the variable x.

 x+y+z=9  xx 2->  2x + 2y + 2z = 18  − 2x+y-z=0  xx 1->  2x + y - z = 0   y + 3z = 18  -> (4)

Select the equations (1) and (3), and eliminate the variable x.

 x+y+z=9  xx 2->  2x + 2y + 2z = 18  − 2x+5y+7z=52  xx 1->  2x + 5y + 7z = 52  - 3y - 5z = -34  -> (5)

Select the equations (4) and (5), and eliminate the variable y.

 y+3z=18  xx 3->  3y + 9z = 54  + -3y-5z=-34  xx 1-> - 3y - 5z = -34   4z = 20  -> (6)

Now use back substitution method

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