Question

What is the solution to the system of equations below:
2x+y-z=5
x+3z=14
-2x-3y+2z=2

Answer 1

u givin me a medal?

Answer 2

um sure. why not.

Answer 3

Well, for starters, you have here a system of three linear equations in three unknowns, which implies that you have enough information to solve for the values of x, y and z.

Answer 4

Which method(s) of solution is/are most familiar to you? Addition/subtraction? Substitution? Cramer's Rule? Matrices?

Answer 5

addition/subtraction i do believe

Answer 6

OK, Princess. Suppose you add the first and third equations together, term by term. The x terms will disappear. Willing to try that?

Answer 7

sure! :D (and yes I am actually a real princess xD)

Answer 8

Is your crown of gold or platinum?

Answer 9

z=3, y=-2, x=5

Answer 10

hheres the workings

Answer 11

silver actually with lots of diamonds.

When I added them together I got -2y+z=7

Answer 12

Trolls will rule better if trolls will let Princess do her own work.
Princess, that first result of yours is perfect.

Answer 13

hahaha I like u mathmale xD

Awesome so what's my next step?

Answer 14

Now, Pricess Silver, please multiply the 2nd equation by 2 and add the resulting equation to the third equation. Again, the x terms will disappear.

Answer 15

Wouldn't it be more helpful to Princess, Troll, if you were to guide her to finding the solution herself?

Answer 16

no, that is just too confusing

Answer 17

just a second

Answer 18

when she want to revise, she will be scrolling up and down

Answer 19

Every Troll is entitled to his/her own opinion.
Of course, Princess!

Answer 20

definitely, just like gandhi

Answer 21

but i am mandela while u are obama, we are both math lovin but different in terms of apporach

Answer 22

So, Princess, you've already obtained -2y + 1z = 7 and are well on your way to obtaining a second equation in y and z only. Please type that equation here when you're finished.

Answer 23

actually, can u generalise this system u talking abt? or do u wanna hear my generalization?

Answer 24

I eagerly await Princess' response.

Answer 25

sorry my mom was talking to me :P

So, mathmale, I did what you said (since i had an explanation sorry trollswillrule but I need this for my final :D) and this is what I got:
(x+3z=14)2= 2x+6z=28
then I added that to -2x-3y+2x=2 and got
-3y+8z=30

Answer 26

Perfect!
So now you have two equations in two unknows:
-2y + 1z = 7
-3y + 8z =30

I'd bet you know how to solve this simpler system.

Answer 27

we would just have to times the first equation by 3 and the second equation by 2 to eliminate y correct?

Answer 28

wait! Times the first equation by -3 so they'll cancel!

Answer 29

Sounds like a great plan, Princess, except use -3 and 2 or 3 and -2. I think the reason for this will become apparent as you go along.

Answer 30

Cool. Great minds think alike.

Answer 31

so z=3... SWEETNESS! I can plug that into x+3z=14 and get x! :D:D:D:D

Answer 32

How cool. Right you are!
Be certain to check your solution (x, -2, 3) into one or more of the original equations to verify that it actually satisfies those equations.

Answer 33

x=5 doesn't it? and they work! We are golden! Yes I might just pass this class after all :P

Answer 34

Good luck on that exam tomorrow!
Invite me to your coronation.

Answer 35

Why thank you! And will do ;) Queen Holli might not be to excited that I'm planning on taking her place as Queen though xD

Answer 36

I haven't actually found x myself. More important to me to help you solve the problem.
Too bad for Q. Holli.

Answer 37

gotcha :D

Truth! lol thanks so much!

Answer 38

My great pleasure. By all means post further questions and perhaps we'll collaborate again. Good night!