2x - 3y - 9z = 11

3x + 3z = - 5

-3x + y - 4z = 8

solve for x, y, z

Step-by-step explanation:

2x - 3y - 9z = 11 ... (1)

3x + 3z = - 5 ... (2)

-3x + y - 4z = 8 ... (3)

add (3) and (2) : y - z = 3 so : y = z+3 (*)

put this value in (1) : 2x-3 (z+3) - 9z = 11

2x-3z - 9-9z = 11 so : 2x = 12z+20

x = 6z+10 ... (**)

put this value in (2) : 3 (6z+10) + 3z = - 5

18z+30+3z=-5

21z = - 35

z = - 35/21 = - 5/3

put this value in (*) and (**) you have x and y.

x = 0, y = 1.333, z = - 1.667 (to the nearest thousandth).

Step-by-step explanation:

2x - 3y - 9z = 11 A

3x + 3z = - 5 B

-3x + y - 4z = 8 C

Multiply Equation C by 3:

-9x + 3y - 12z = 24 D

Adding A + D:

-7x - 21z = 35 Divide by 7:

-x - 3z = 5 E

Adding B + E:

2x = 0

x = 0

Plugging in x = 0 into equation B:

3 (0) + 3z = - 5

z = - 5/3

z = - 1.667

Now plugging the values of y and z into equation A:

2 (0) - 3y - 9 (-5/3) = 11

-3y = 0 + 11 + 9 (-5/3) = - 4

y = 4/3 = 1.333.