Question

6x-6y-4z=-10, -5x+4y-z=-12 and 2x+3y-2z=9.

Answer 1

Elimination method

Given first equation 6x-6y-4z = -10 ---> (1)

Second equation -5x+4y-z = -12

Multiple to each side by negitive 4

20x-16y+4z = 48 ---> (2)

Third equation 2x+3y-2z = 9

Multiple to each side by negitive 2.

-4x-6y+4z = -18 ---> (3)

To eliminate the z value add the equations (1)&(2).

6x-6y-4z = -10

20x-16y+4z = 48

______________

26x-22y = 38 ---> (5)

To eliminate the z value add the equations (1)&(3).

6x-6y-4z = -10

-4x-6y+4z = -18

_____________

2x-12y = -28

Multiple to each side by negitive13.

-26x+156y = 364 --->(6)

To eliminate the x value add the equations (5)&(6).

26x-22y = 38

-26x+156y = 364

_______________

134y = 402

Divide to each side by 134.

y = 3

Substitute the y value in (1)&(2).

6x-18-4z = -10

6x-4z = 8 ---> (7)

20x-48+4z = 48

20x+4z = 96 ---> (8)

To eliminate the z value add the equations (7)&(8).

6x-4z = 8

20x+4z = 96

__________

26x = 104

x = 4

Substitute x,y in (1).

24-18-4z = -10

6 - 4z = -10

-4z = -16

z = 4

Solution x = 4, y = 3, z = 4.