2x-3y+4z=19
x-2y+z=9
3x-y+2x=10
x = 2y-z+9, so
2(2y-z+9)-3y+4z = 19
3(2y-z+9)-y+2z = 10
or
y+2z = 1
5y-z = -17
y = -2z+1, so
5(-2z+1)-z = -17
-11z = -22
z = 2
y = -3
x = 1
x-2y+z=9
3x-y+2x=10
2(2y-z+9)-3y+4z = 19
3(2y-z+9)-y+2z = 10
or
y+2z = 1
5y-z = -17
y = -2z+1, so
5(-2z+1)-z = -17
-11z = -22
z = 2
y = -3
x = 1