Solve it using elimination substitution or GaussJordan elimi

Solve it using elimination, substitution, or Gauss-Jordan elimination on a matrix. Show work.

5x + 3y + z = -3

x - 3y + 2z = -24

14x - 2y + 3z = -71

elimination method :

5x + 3y + z = -3--------->(1)

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

14x - 2y + 3z = -71------------->(3)

(1)+(2)

6x +3z =-27

=>2x +z =-9----------->(4)

(2)*1 +(3)*2

2*(5x + 3y + z) +(14x - 2y + 3z)*3= -6-216

10x+6y +5z+42x-6y+9z=-222

52x +14z =-222

26x +7z =-111-------------->(5)

(5)- 7*(4)

(26x +7z)-7*(2x +z )=-111-7*(-9)

26x +7z -14x -7z =-111+63

12x =-48

x =-4

put x =-4 in (4)

2(-4) +z =-9

-8+z =-9

z =-9+8

z =-1

put x =-4, z =-1 in (1)

5*(-4) + 3y -1 = -3

-20+3y-1=-3

3y=18

y =6

so solution is x=-4,y=6,z=-1