subtract the first equation from the second one, then divide the second equation by -2; subtract the first equation multiplied by 2 from the third one:

x + 2y - z = -10

y - z = -5

-5y + z = 5

add the second equation multiplied by 5 to the third equation:

x + 2y - z = - 10

y - z = -5

- 4z = - 20

Then from the last equation z = -20/-4 = 5, from the second equation y = z -5 = 0, from the first equation