#color(green)("Three given equations are") #
#x+2y+z=34.......(1)#,
#x+2y+2z=38.......(2)#,
#2x+y+3z=54......(3)#
#color(blue)("Subtracting (1) from(2) we have") #
#x+2y+2z-(x+2y+z)=38-34#
#=>cancelx+cancel(2y)+2z-cancelx-cancel(2y)-z=4#
#=>z=4#
#color(blue)("Inserting the value of z in (1)") #
#x+2y+4=34#,
#x+2y=30.....(4)#
#color(blue)("Inserting the value of z in (3)") #
#2x+y+3xx4=54#
#2x+y =42.......(5)#
#color(blue)("Multiplying (4) by 2 and subtracting the resulting equation from (5)") #
#2x+y -2xx(x+2y)=42-2xx30#
#=>2x+y -2x-4y=42-60#
#=>-3y=-18#
#=>y=6#
#color(blue)("Inserting the value of y in (4) "#
#x+2xx6=30#
#=>x=18#