We are asked to solve a system of three linear equation in three unknowns (x, y, and z)
Eq 1) 5 x + 9 y + 10 z = -8
Eq 2) 6 x + y + z = 0
Eq 3) 6 x - y - z = 0
So we start by combining Eq 2 and 3 as they are. Adding term by term each side of the equal sign:
6 x + y + z + 6 x - y - z = 0+ 0
12 x + 0 + 0 = 0
12 x = 0
then x = 0/12 = 0
So x is zero
and then we can find y in terms of z using either Eq 2 or Eq 3:
6 (0) + y + z = 0
then
y = -z
Now we use the values : x = 0 and y = - z in Eq 1):
5 (0) + 9 (-z) + 10 z = -8
0 - 9 z + 10 z = -8
z = -8
So we found the three values:
x = 0, y = - z = -(-8) = 8, and z = -8
x = 0, y = 8 , and z = -8