Question

Solve Algebraically
x-3y+4z=7
2x+2y-3z=-3
x-3y+z=-2

Answer 1

what variable are we solving for?

Answer 2

I believe all of them. All the instructions say was solve Algebraically so I think I have to find one variable at a time to ultimately find them all

Answer 3

interesting...the best way to solve for a variable is, of course, to isolate it.

Answer 4

wait...does this problem mention anything about solving a system of equations?

Answer 5

because, if you have to solve for each variable...we're going to have to use a multitude of techniques. For example, let me show you an example of what I mean by "isolating the variable."

Answer 6

x-3y+4z=7
^
this is your first equation, is it not?
since x is already by itself, this should be relatively easy to solve for!

x-3y+4z=7
+3y +3y
------------
x+4z=7+3y
-4z -4z

x=7+3y-4z

We get that x is equal to 7+3y-4z by isolating x in the first equation. Make sense so far?

Answer 7

@BinkyBoo you following me so far? :)

Answer 8

Yes I think I am

Answer 9

alright.

So do you think you can solve for any other variables for any other equations?
Hint: you can isolate for something in the 3rd equation

Answer 10

couldn't I isolate the x again?

Answer 11

x y z, the alg2 fun xD

Answer 12

you could. but you could also isolate for z.

The more things you isolate for, the easier of a time we'll have substituting them in later and lol @ShadowLegendX indeed

Answer 13

So then if i have one isolated for x and then one for z then I have to get one for y still right?

Answer 14

true..but y is not so easily isolated. this is where we have to start substituting

Answer 15

so we're going to multiply the third equation by 2, which gives us
2x + 4y - 6z = 2
^
then, we add this to the first equation:
-2x + 3y + z = 3
2x + 4y - 6z = 2
---------------------
7y - 5z = 5

Answer 16

^^now that we have that narrowed down to two variables, we need to multiply the third equation by -3. What does that give us?

Answer 17

@BinkyBoo

Answer 18

Need a little more guidance, perhaps? lol don't leave me hanging here

Answer 19

I'm sorry I'm trying to make sure I wasn't missing some other instructions because it seemed so vague
it would give us 3x-9y+3z=-6

Answer 20

I think I am understanding now.

Answer 21

right! You just keep substituting, finding common variables until you're able to solve for your first variable! Once you have that variable, the rest should be piece of cake.

Answer 22

AHHHHH THANK YOU SO MUCH!!!!!! :D

Answer 23

no problem! <3

Answer 24

think of it as one gigantic puzzle ^_^ LOL been a while since I had a problem like this to solve! But once you crack the code, it should come quite easily

Answer 25

@Jamierox4ev3r well explained!

Answer 26

thank you :)

In fact @BinkyBoo I can share with you an even quicker way of doing this! I just found it out, working by scratch

Answer 27

so if you multiply the first equation by -1, what do you get?

Answer 28

you get -x+3y-z

You can then add this to the 1st equation, which gives you the following:

x-3y+4z=7
-x+3y-z=2
----------
3x=9

and here, you can easily solve for x! Now that you have a value for x, you can plug it in to the rest of the equations to solve for x and y ^_^ I hope you find this method even easier

Answer 29

Oh my gosh! how did I not see that at first haha thank you you broke this down perfectly!!!

Answer 30

no problem x'D sometimes, negatives can be our best friends. Especially when they help eliminate variables that we don't want