here we have given three system of linear equations.
x+y+z=-6
-2x-2y-2z=12
5x+5y+5x=-30.
here three unknowns will have same value x=y=z .
the x+y+z=-6
x+x+x=-6=3x=-6,x=-2
we know that x=y=z .
then x=-2 y=-2 and z=-2.
for part b we have three equation x+y=6
y+z=0
x+y-z=0
we need to use substitution method.
in second equation we have y+z=0 it mean y=-z
we need to plug y=-z in any one of the equation to find other value.
in first equation we have x+y=6 it becomes x-z=6
then in third equation we have x+y-z=4 we will rewrite this as x-z+y=4
we know that x-z=6
so 6+y=4
y=-2
y+z=0 =-2+z=0
z=2
we know x+y=6
x+(-2)=6=x=8.
x=8 y=-2 z=2
