x+4y+z=3 ————(1)
Make x the subject of the rule in (1)
:- x=-4y-z ————(2)
2x+y+z=11 ————(3)
Substitute (2) in (3)
2(-4y-z)+y+z=11
-8y-2z+y+z=11
-7y-z=11
-z= 11+7y
z= -11+7y ————(4)
4x+y+2z=23 ————(5)
Substitute (2) & (4) in (5)
4(-y-z)+y+2(-11+7y)=23
-4y-4z+y-22+14y=23 ————(6)
Substitute (4) in (6)
-4y-4(-11+7y)+y-22+14y=23
-4y+44-28y+y-22+14y=23
-17y+22=23
17y=22-23
17y=-1
y=-1/17 ————(a)
Substitute (a) in (4)
z=-11+y
z=-11+-1/17
z=(-187-1)/17
z=-188/17 ————(b)
Substitute (a) & )b) in (2)
x=-4y-z
x=-4(-1/17)-188/17
x= 4/17-188/17
x=-184/17 ————(c)
To make sure substitute (a),(b)&(c) in 1
x+4y+z=3
-184/17+4(-1/17)+2(-188/17)=3