Question

PLEASE HELP! WILL GIVE MEDAL TO BEST ANSWER.
@mathmate
Solve the system using substitution.
{-x-y-z=-8
{-4x+4y+5z=7
{2x+2z=4

Answer 1

Nevermind, @mathmate isn't online. Anyone else want to help???

Answer 2

may i?

Answer 3

Yes, of course! :D

Answer 4

The solution set I got was (2,7,-1) and it's wrong, so I'm getting really frustrated right now...

Answer 5

is it must use substitution only?

Answer 6

Yep.

Answer 7

Well, I'm supposed to show my work, so if I do it another way it'll probably be marked wrong...

Answer 8

Oh hello, @mathmate ! You helped me before so I thought you could help me with another one!

Answer 9

Examine the equations and decide which is the best one to use for substitution!

Answer 10

The first equation is, I'm pretty sure. I reduced it down to z=8-y-x

Answer 11

You are substituting one variable with two other ones.

What if you take
(3)/2 which gives x+z=2
Transpose the x to the right gives
z=2-x .......(4)

Substitute z (from (4)) into (1) and (2) and the trick is done.
You end up with two equations with unknowns x and z.

Answer 12

-y+8=x+z |2

-2y+16= 2x+2z

Answer 13

*x and y

Answer 14

Wait... so you're dividing the 3rd equation by 2 @mathmate ?

Answer 15

yes, there is a common factor of two.

Answer 16

Hmmm... that's a different way to do it! Never would've thought of doing it that way! I'll try it your way now and see what happens...

Answer 17

What you suggested is ok too! But it might be a little more arithmetic operations.

Answer 18

When I tried it my way, I got mostly decimals. So I got really annoyed with the equation I chose...

So when I plug (z=2-x) into -x-y-z=-8, is there any distributing involved?

Answer 19

First, i would change -x-y-z=-8 to
x+y+z=8 (life is easier that way).
Then
x+y+(2-x)=8
That gives y=6 right away! lol

Answer 20

But are you really allowed to get rid of all the negative signs like that? o_o

Answer 21

Yes, basically you multiply both sides by -1.

Answer 22

Wow, okay! I wish I knew as many little tricks like that! Okay, so now how do I figure out the other 2 variables? I forgot...

Answer 23

Call
y=6 ..............(5)
Substitute (4) and (5) in (2) to find x.

Substitute this value of x into (4) to find z.

Answer 24

Okay, I'll do that and see what I get...

Answer 25

THe best trick is to write down the equations (and the numbers like .......(4)) neatly in order, then you'll find your way.

Answer 26

I got: (3, 6, -1)

Answer 27

That's perfect.
Another trick is to substitute what you've got back into equations (1), (2) and (3) and check that they all work.
This is an exam saver! :)

Answer 28

Yep, I just checked, and it's right! Yay, thanks for helping me solve another one! You're the best! :D
Could you help me with another couple of questions...?

Answer 29

Sorry, I have to go.
However, I love to give you a medal because for the longest time I haven't worked with someone who is actually interested in working out the problems!
You're the best!

Answer 30

Aw, alright! I guess I'll have to post another question on here and wait for someone to help...

Aww, thanks! I appreciate it! I'll write a testimonial for you once I get the chance! :D

Answer 31

Oops, I didn't mean to post that screenshot. That's the problem I was gonna ask for help for. Just ignore that! :)