Question

3x-2y+z=9

x-y+4z=10
2x+3y-z=53

Answer 1

besides a calculator solution? Your calculator should be able to solve these.

Manually:
add the first and third equations:
5x+y=62

multipy the first equation by 4
12x-8y+4z=36 and subtract equation 2 from that, or
11x-7y=26, and combine that with the original combination:

11x-7y=26
6x+y=62

now multipy the second equation by 7, then add the equations.