Question

2x – 3y - 9z = 11
3x + 3z= – 5
-3x + y - 4z = 8
solve for x,y,z​

Answer 1

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 .

Answer 2

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

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.