S1 -> 3x + y – z = -5

S2 -> -4x + y = 6

Now eliminate y from S2:

S4 -> S2 – S1

-> -4x + y – (3x + y – z) = 6 – (-5)

-> -4x + y – 3x – y + z = 6 + 5

->-7x + z = 11

S3 -> 6x – 2y + 3z = 2

Now eliminate y from S3:

S5 -> S3 + 2S1

-> 6x – 2y + 3z + 2(3x + y – z) = 2 + 2(-5)

-> 6x – 2y + 3z + 6x +2 y – 2z = 2 – 10

-> 12x + z = -8

Now eliminate z from S5 and solve for x

S5 – S4

12x + z – (-7x + z) = -8 – 11

12x + z + 7x – z = -19

19x = -19

x = -19/19

x = -1

Now plug in x into S5 and solve for z

12x + z = -8

12(-1) + z = -8

-12 + z = -8

z = -8 + 12

z = 4

Now plug in x into S2 and solve for y

-4x + y = 6

-4(-1) + y = 6

4 + y = 6

y = 6 – 4

y = 2

I hope this helped

Kia