ANSWER
[tex]x=3,y=6,z=-1[/tex]
EXPLANATION
We the have the equations,
[tex]-x-y-z=-8[/tex]
Multiplying through by negative one gives,
[tex]x+y+z=8---(1)[/tex]
Also
[tex]-4x+4y+5z=7---(2)[/tex]
and
[tex]2x+2z=4[/tex]
Dividing through by 2 gives
[tex]x+z=2[/tex]
Making z the subject gives,
[tex]z=2-x---(3)[/tex]
Now we substitute equation (3) into equation (1) and (2)
Equation (3) in to equation (1) gives,
[tex]x+y+2-x=8[/tex]
This implies that;
[tex]y=8-2[/tex]
[tex]y=6[/tex]
We now put equation (3) in (2) to get,
[tex]-4x+4y+5(2-x)=7[/tex]
This implies that
[tex]-4x+4y+10-5x=7[/tex]
[tex]-9x+4y=7-10[/tex]
[tex]-9x+4y=-3[/tex]
But
[tex]y=6[/tex]
So,
[tex]-9x+4(6)=-3[/tex]
[tex]-9x+24=-3[/tex]
[tex]-9x=-3-24[/tex]
[tex]-9x=-27[/tex]
Dividing through by negative 9 gives
[tex]x=3[/tex]
and
[tex]z=2-3[/tex]
[tex]z=-1[/tex]
Therefore [tex]x=3,y=6,z=-1[/tex]
