Question

I need help understanding this:
If you were to use the substitution method to solve the following system, choose the new system of equations that would result if x was isolated in the second equation.
5x - 2y - z = 16
x + y + 4z = 6
3x + 2y + 6z = 16
Thanks!

Answer 1

from second equation
x = 6 - y - 4z

now plug this for x into equations 1 and 3

Answer 2

So, something like 5( 6-y-4z)=16?

Answer 3

and 3( 6-Y-4Z) + 2y + 6z = 16? And then would I distribute those?

Answer 4

yes

Answer 5

for the first one its 5(6 - y - 4z) -2y - z = 16

Answer 6

So for the first one I would get 30 - 5y - 20z + 16???

Answer 7

oh

Answer 8

no you missed out the -2y - z

Answer 9

So, 30 - 5y - 20z - 2y -z = 16?

Answer 10

yes
and that simplifies some more to
30 - 7y - 21z - 16 = 0
14 - 7y - 21z = 0

Answer 11

My options are
a) -3y +19z = -14
5y +18z =-2
b) 7x +7z =28
x-2z=4
c) -7y-21z=-14
-y-6z=-2
d) 21x - 7y=70
33x-10y=112
I got the simplified version you wrote but how do I get to one of the answers

Answer 12

or if you prefer it with a number on RHS:
7y + 21z = 14

Answer 13

right well my equation is really the same as the first one in c)

Answer 14

Okay and the second part of the equation in c is just a simplified version?

Answer 15

i'm checking that one now
3( 6-Y-4Z) + 2y + 6z = 16?

18 -3y - 12z +2y + 6z = 16
18 - y - 6z = 16
-y - 6z = -2

yup c) is the correct option

Answer 16

Thanks so much :)!

Answer 17

yw