Question

Solving Systems of Equations with three variables via substitution?

z = 3x + 5y - 17
-2x - y + 3z = 12
-3x + 3z = 12

Mahalo nui loa~

Answer 1

I don't think this can be solved using substitution. You just go round in circles - atleast that's what I have done for the past 15 minutes.

Answer 2

but,
x=3
y=3
z=7

Answer 3

Yeah, I kinda went around in circles as well. I'm not sure why it was asking to use substitution. But thank you again, Chaise :). Sorry for all the trouble! >.<;;

Answer 4

\[z = 3x + 5y - 17\]\[-2x - y + 3z = 12\]\[-3x + 3z = 12\]
\[3x + 5y -z= 17\]\[-2x - y + 3z = 12\]\[-3x + 3z = 12\]
Substract\[-3x + 3z = 12\]from
\[-2x - y + 3z = 12\]that gives you
\[x-y=0\rightarrow x=y\]Now, let's take \[3x + 5y -z= 17\]and substitute x with y, we get\[3x+5x-z=17\rightarrow z=8x-17\]Lets go back to \[-2x - y + 3z = 12\]and replace everything we know so far, that is x=y, z=8x-17\[-2x - x + 3(8x-17) = 12\]\[21x=63\rightarrow x=3\rightarrow y=3\]Don't forget \[z=8x-17\]replacing x with 3\[z=8\times3-17\rightarrow z=7\]Finally, \[(x,y,z)=(3,3,7)\]

Answer 5

good

Answer 6

Thank you Kmousou! :D

Answer 7

Uhh hey Kmousou, I don't mean to be a pest but wanna help me out with another problem similiar to this?