2x+y-z=7, x-2y+2z=-9 and 3x-y+z=5

Question

find x ,y , z.

Answer 1

Elimination method :

Given equations are 2 x + y - z = 7 ---> (1)

x - 2 y + 2 z = -  9 ----> (2)

3 x - y + z = 5 ----> (3)

Multiply each side by - 2  in eq ( 2)

We get the equation - 2 x + 4 y - 4 z  = 18  ---------> ( 4 )

To eliminate the y & z  values  add  (1)&(4).

2 x + y - z = 7

- 2x + 4y - 4 z  = 18
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5y - 5 z = 25 -------------> ( 5 )

Multiply each side by - 3  in eq ( 2)

We get the equation - 3x + 6 y - 6z  =   27------> ( 6 )

To eliminate the x value  add (3)&(6).

3x - y + z = 5

- 3x + 6 y - 6z  =   27

______________

5 y - 5z = 32   ---> (7)

Subtract the eq ( 5 ) & ( 7 ) 

5y - 5 z = 25

5 y - 5z =32    ( change the symbols )

_____________

0 - 0 = - 7

0 = - 7

Therefore statement is false.

So the system of equations has no solutions.