System of equations

Question

Given the system of equations:

2x−3y−9z=6

x+3z=

6−3x+y−4z=−16

(a) Determine the type of system: dependent (which is right)

(b) If your answer is dependent in (a), find the complete solution.

Write x, y as functions of t, where z=t

If your answer is inconsistent, write DNE for all three variables.

x= 

y=  

z= 

I get lost on the second part because when I solve this, I end up missing Y or z

Answer 1

2x-3y-9z=6

x+3z=6

-3x +y-4z =-16

use substitution, elimination or matrix algebra

2nd times 3, add to 3rd

y+5z = 2

2nd times 2, subtract from 1st

-3y -15z =-6 is

-3(y+5z=2)

dependent system of equations, infinite solutions