Answer:
[tex]x=1,y=3,z=1[/tex]
Step-by-step explanation:
[tex]4x-4y+4z=-4[/tex]
[tex]4x=-4+4y-4z[/tex]
[tex]x=-1+y-z[/tex]
Substitute [tex]x=-1+y-z[/tex] into second equation:
[tex]4\left(-1+y-z\right)+y-2z=5[/tex]
[tex]-4+4y-4z+y-2z=5[/tex]
[tex]5y-6z-4=5[/tex]
[tex]y=\frac{6z+9}{5}[/tex]
Substitute [tex]x=-1+y-z[/tex] and [tex]y=\frac{6z+9}{5}[/tex] into the third equation:
[tex]\frac{-41z-54}{5}+3=-16[/tex]
[tex]-41z-54=-95[/tex]
[tex]z=1[/tex]
Substitute [tex]z=1[/tex] into [tex]y=\frac{6z+9}{5}[/tex]:
[tex]y=3[/tex]
Plug in y and z values into [tex]x=-1+y-z[/tex]:
[tex]x=1[/tex]
