Find the Solution Set

Question

Find the Solution Set of the System

x+2y+3z=0

x-2z=3

y+z=1

 

I've tried using substitution, however, plugging the answers back in never worked. Please show me how to solve this problem, in form of (x,y,z)

Answer 1

So first solve y+z=1 for y, and you get y=1-z.

 

Next, solve x-2z=3 for x, and you get x=3+2z.

 

Now substitute both into the first equation:

 

(3+2z)+(2)(1-z)+3z=0

 

3+2z+2-2z+3z=0

 

combine like terms:

 

3z+5=0

 

z=-5/3

 

 

Now you can solve for the rest:

 

y+z=1

 

y-5/3=1

 

y=8/3

 

and

 

x-2z=3

 

x-(2)(-5/3)=3

 

x+(10/3)=3

 

x=3-(10/3)

 

x= -1/3

 

 

So you have x=-1/3  ,  y=8/3   , z=-5/3

 

Your final answer would be (-1/3,8/3,-5/3) 

 

Let me know if you need any other help!