system of equations for x,y, and z

Question

The question is 

 

3x=2y-z=4

2x-y+2z=10

x+3y-4z=-7

 

 

I made a mistake on one part but cant seem to find it 

 

Answer 1

3x -2y -z = 4

2x -y +2z = 10

x +3y -4z = -7

use substitution, elimination or matrix algebra

multiply 2nd equation by 2, then subtract 1st equation

4x-2y+4z = 20

3x-2y-z = 4

x +5z = 16

multiply 2nd by 3, then add 3rd equation

6x -3y +6z = 30

x + 3y-4z = -7

7x +2z = 23

7x +35z = 112

33z = 89

z =89/33

x= 16-5(89)/33

y = 2(89/33)+32 -10(89/33) -10

or maybe you meant

3x +y +2z = 4

2x -y +2z = 10

x +3y - 4z =-7

then

5x +4z = 14

6x -3y +6z =30

7x +2z = 23

14x +4z = 46

9x = 32

x = 32/9

z =23/2 -7(16)/9 = 207/18 -224/18 = -17/18

y = 2z+2x-10 = -17/9 +64/9-10= 47/9-90/9 =-43/9

(x,y,z) = (32/9,-43/9, -17/18)