NEED HELP IN MATHS!! Please help!

find x, y and z

x - z = -5
2x+3y+2z=12
x+y+3z=13

use row reductions

[1, 0, -1, -5]
[2, 3, 2, 12]
[1, 1, 3, 13]

add 2 times first row to second

[1, 0, -1, -5]
[0, 3, 4, 22]
[1, 1, 3, 13]

add -1 times first row to third

[1, 0, -1, -5]
[0, 3, 4, 22]
[0, 1, 4, 18]

multiply second row by 1/3

[1, 0, -1, -5]
[0, 1, 4/3, 22/3]
[0, 1, 4, 18]

add -1 times second row to third

[1, 0, -1, -5]
[0, 1, 4/3, 22/3]
[0, 0, 8/3, 32/3]

multiply 3rd row by 3/8

[1, 0, -1, -5]
[0, 1, 4/3, 22/3]
[0, 0, 1, 4]

add -4/3 times 3rd row to the 2nd

[1, 0, -1, -5]
[0, 1, 0,2]
[0, 0, 1, 4]

add 3rd row to 1st

[1, 0, 0, -1]
[0, 1, 0,2]
[0, 0, 1, 4]

x=-1
y=2
z=4

Use equation 1 to express x in terms of z by adding z to both sides:

x = z - 5

Substitute z - 5 for x in the other two equations:

2(z - 5) + 3y + 2z = 12

(z - 5) + y + 3z = 13

Simplify both equations:

1) 2z - 10 + 3y + 2z = 12

4z - 10 + 3y = 12

4z + 3y = 22


2) (z - 5) + y + 3z = 13

4z - 5 + y = 13

4z + y = 18

Subtract the second from the first:

4z + 3y = 22
-(4z + y = 18)
-----------------
2y = 4

y = 2

Substitute 2 for y and solve for z:

4z + y = 18

4z + 2 = 18

4z = 16

z = 4

Since x = z - 5:

x = 4 - 5 = -1


x = -1, y = 2, z = 4