Solve x + y + z = - 6

-2x - 2y - 2z = 12

5x + 5y + 5z = - 30

Solve x + y = 6

y + z = 0

x + y - z = 4

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