2x - 3y - 9z = -32
x + 3z = 8
-3x + y - 4z = -8
Add all the equations together.
-3y - 10z = -32
By looking at the first equation, 2x - 3y - 9z = -3y - 10z.
So 2x = -z.
By looking at the second equation, x + 3z = (-0.5z) + 3z = 8.
So 2.5z = 8, and z = 3.2.
This means that x = -1.6.
Let's substitute into our original equations!
-3.2 - 3y - 28.8 = -32
4.8 + y - 12.8 = -8
Therefore, y = 0!
Since these answers do not contradict each other, they are dependent.
The answers are x = -1.6, y = 0, z = 3.2.
