SOLUTION: Please help me and show steps. I never been good doing these. Given the system of equations 2x-3y-9z=-5 x+3z=5 -3x+y-4z=-10 (a) determine whether the system is inconsi

Question 1025532: Please help me and show steps. I never been good doing these.

Given the system of equations
2x-3y-9z=-5
x+3z=5
-3x+y-4z=-10
(a) determine whether the system is inconsistent or dependent;
Your answer is (input inconsistent or dependent)
(b) if your answer is dependent in (a), find the complete solution. Write x
and y as functions of z.

x=
y=

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
2x-3y-9z=-5
x+3z=5
-3x+y-4z=-10
--------------
The 2nd eqn has no y term, so eliminate y using the 1st and 3rd eqns.
2x-3y-9z=-5
-3x+y-4z=-10 times 3 --> -9x+3y-12z = -30
-----
2x -3y-9z=-5
-9x+3y-12z = -30
------------------- Add
-7x - 21z = -35
Divide by -7
x + 3z = 5
That's the same as eqn 2 --> dependent, no unique solution
----
(b) if your answer is dependent in (a), find the complete solution. Write x
and y as functions of z.
----
x = 5 - 3z
y = 5 - 5z
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