Given data:
The first equation is 5x-4y+2z=21.
The second equation is -x-5y+6z= -24.
The third equation is -x-4y+5z=-21.
Multiply 5 by second equation and add first and second equation.

Multiply 5 by third equation and add first and second equation.

Substitute the above value of z in equation(A).

The value of z is,

The value of x is,

Thus, the value of x is 5, the value of y is -1, and the value of z is -4.