Three Variable Systems x+y+z=-8 2x+5y+2z=-34 -x+7y-3z=-38

Question

x+y+z=-8

2x+5y+2z=-34

-x+7y-3z=-38

Answer 1

Elimination method :

Given equations are x + y + z = - 8  ---> (1)

2 x + 5 y + 2 z = - 34  ----> (2)

- x + 7y - 3z =- 38---> (3)

multiply each side by - 2   eq ( 1 )

We get  the equation  - 2 x  - 2 y  - 2 z  = 16 ------ > ( 4 )

To eliminate the x & z  values add  (2)&(4).

2 x + 5 y + 2 z = - 34

- 2 x  - 2 y   - 2 z  =  16

_______________

3 y  =  - 18

y  =  -  6

multiply each side by 2 eq ( 3)

We get the equation   -  2 x  + 14 y -  6 z  =  -  76 ------> ( 5 )

To eliminate the x  value add  (2)&(5).

2 x + 5 y + 2 z      = - 34

- 2 x  + 14 y - 6 z = - 76

___________________

19y -4 z = -110 ---> (5)

Substitute y value in eq ( 5 )

19 ( - 6) - 4 z = - 110

- 114 - 4 z  =  -  110

- 114 + 110  =  4 z

- 4  =  4 z

- 1 = z

z  = - 1

Substitute the y & z values in eq ( 1 )

x + y + z = - 8

x + ( - 6 ) + ( - 1 ) = - 8

x - 7 = - 8

x = - 8 + 7

x = - 1.

Therefore  x = - 1 , y  = - 6 , z  =  - 1.