Help me solve the system below?

3x - 5y + 2z = -53 …… [1]
x - 7y - 4z = -37 …… [2]
5x + 9y + 2z = 57 …… [3]

[1] × 2:  6x - 10y + 4z = -106 …… [4]
[2] × 2:  10x + 18y + 4z = 114 …… [5]

[2] + [4]:  7x - 17y = -143 …… [6]
[2] + [5]:  11x + 11y = 77
                x + y = 7
                y = 7 - x …… [7]

Plug [7] into [6]:  7x - 17(7 - x) = -143
                           24x = -24
                           x = -1

Plug x = -1 into [7]:  y = 7 - (-1)
                                y = 8

Plug x = -1 and y = 8 into [2]:  (-1) - 7(8) - 4z = -37
                                                -4z = 20
                                                z = -5

Hence, (x, y, z) = (-1, 8, -5)

3x - 5y + 2z = -53
x - 7y - 4z = -37 
5x + 9y + 2z = 57
Solution:
x = -1, y = 8, z = -5

3x - 5y + 2z = -53 and x - 7y - 4z = -37 and 5x + 9y + 2z = 57

Since the only coefficient of 1 we have is the "x" in the second equation, let's solve for that in terms of "y" and "z" so we can then substitute it into the other two equations:

x - 7y - 4z = -37
x = 7y + 4z - 37

3x - 5y + 2z = -53 and 5x + 9y + 2z = 57
3(7y + 4z - 37) - 5y + 2z = -53 and 5(7y + 4z - 37) + 9y + 2z = 57
21y + 12z - 111 - 5y + 2z = -53 and 35y + 20z - 185 + 9y + 2z = 57
16y + 14z - 111 = -53 and 44y + 22z - 185 = 57
16y + 14z = 58 and 44y + 22z = 242

The first equation can be divided by 2 and the second by 22 to simplify:

8y + 7z = 29 and 2y + z = 11

Now we can solve for "z" in terms of "y" in the second equation and substitute one more time:

2y + z = 11
z = 11 - 2y

8y + 7z = 29
8y + 7(11 - 2y) = 29
8y + 77 - 14y = 29
-6y + 77 = 29
-6y = -48
y = 8

Now we can start working back and solving for "z" and "x":

z = 11 - 2y
z = 11 - 2(8)
z = 11 - 16
z = -5

x = 7y + 4z - 37
x = 7(8) + 4(-5) - 37
x = 56 - 20 - 37
x = -1

The answer to this system of equations is:

x = -1, y = 8, and z = -5