x-y+z=4, 2x-6y-3z=24 and 3x-4y+2z=7

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Answer 1

  

Elimination method :

Given equations are  x - y + z = 4  ---> (1)

2 x - 6 y - 3 z = 24 ----> (2)

3 x -4 y + 2 z = 7  -----> (3)

Multiply each side by - 2  in eq ( 1)

We get the equation - 2 x + 2 y -  2 z  = - 8  ---------> ( 4 )

To eliminate the x  value add  (2)&(4).

2 x - 6 y - 3 z = 24 

- 2 x + 2 y -  2 z  = - 8

________________

- 4 y - 5 z =  16---> ( 5 )

Multiply each side by - 3  in eq (2 )

We get the equation - 6 x + 18 y + 9 z  = - 72 --------> ( 6 )

Multiply each side by 2 in eq (3)

We get the equation 6 x - 8 y + 4 z  = 14--------> ( 7 )

To eliminate the x  value add (6)&(7).

- 6 x + 18 y + 9 z  = - 72

6 x - 8 y + 4 z  = 14

_________________

10 y + 13 z = - 58 -----> (8)

Multiply each side by  10 in eq (5 ) 

We get the equation - 40 y - 50 z = 160 -------> ( 9 )

Multiply each side by  4  in eq (8 ) 

We get the equation 40 y +52 z = - 232 -------> (10 )

To eliminate the y value add (9)&(10).

- 40 y - 50 z = 160

40 y +52 z = - 232

_____________

2 z =  - 72

z = - 72 / 2 = - 36

z =- 36

Substitute the z value in eq ( 5 ).

- 4 y - 5 z =  16

- 4 y - 5 (- 36 ) =  16

- 4 y +180 = 16

- 4 y =  16 - 180

- 4 y  = - 164

 y  = - 164 / - 4 =  41

y =  41

Substitute the values z  & y values in eq ( 1 )

x - y + z = 4

 x - 41  -  36  = 4

 x - 41  - 36  = 4

x - 77 = 4

x = 4 +77 = 81

x = 81.

Solution of the system of  the equations is x = 81  y  =  41 and  z = - 36.