x+2y-6=z, 3y-2z=74, 4+3x=2y-5z rearrange all to the form ax+by+cz=n
x+2y-z=6, 3y-2z=74, 3x-2y+5z=-4
eliminate x from the 1st and 3rd equations...
-3(x+2y-z=6)+(3x-2y+5z=-4)
-3x+3x-6y-2y+3z+5z=-18-4
-8y+8z=-22 and the 2nd equation was 3y-2z=7, now we can eliminate z
(-8y+8z=-22)+4(3y-2z=7)
-8y+12y+8z-8z=-22+28
4y=6
y=1.5, making 3y-2z=7 become:
3(1.5)-2z=7
4.5-2z=7
-2z=2.5
z=-1.25, making x+2y-z=6 become
x+2(1.5)-(-1.25)=6
x+3+1.25=6
x+4.25=6
x=1.75
So (x,y,z)=(1.75, 1.5, -1.25)