Question

Solve: x – 3y + z = 10
x + y – 3z = -10
-3x – y + z = 2 write your numeric answers as an ordered triple: (x,y,x)

Answer 1

Do you know how to start?

Answer 2

?

Answer 3

nope sorry i was helping my little brother. i have no clue how to do this at all

Answer 4

Okay. Read this carefully.

Take 2 equations. Let's say 1 and 2.
Solve them for "z".
Equate them.
(You'll get a polynomial without z then).

Second, again take 2 equations. Let's say 2 and 3.
Solve them for z.
Equate them.
(You'll get a polynomial without z then).

Solve both of them simultaneously.

Answer 5

ok can i show you my work to make sure i am doing it right?

Answer 6

do i cancel the z's out so i multiply the equation 1 by 3 to get the z's the same to be able to cancel them.

Answer 7

No. That can get you wrong. Solve this way.

Answer 8

LOOK:

x – 3y + z = 10
x + y – 3z = -10
-3x – y + z = 2

eq 1 and eq 2

z = 10 + 3y -x z= (x+y+10)/3

Do you get till here?

Answer 9

kind of i understand you moved the z behind the = sign but how do you do that?

Answer 10

I did it in one step, mentally.
I'll show you how i did that for equation 2 so you can get an idea:
x + y – 3z = -10
y - 3z = -10 - x
-3z = -10 -x -y
3z = 10 + x + y

z = (10 + x + y)/3

Answer 11

that makes since ok

Answer 12

what do i do after that though

Answer 13

Okay. Now read my explanation again.
I said: "Equate them.
(You'll get a polynomial without z then)."
z = 10 + 3y -x z= (x+y+10)/3

10 + 3y - x = (x+y+10)/3

Answer 14

ok i got that so now what how do you zolve for it now?

Answer 15

Write it in the simplified form:
2y - 2x = -5

Now you can see that there's no z.

NOW take 2 more equations and do all of this again.

Answer 16

how did you simplify it like that though

Answer 17

10 + 3y - x = (x+y+10)/3

Multiply 3 on both sides and then isolate x and y on left side.

Answer 18

that confuses me.....

Answer 19

Why? Where?

Answer 20

like the whole simplifying step confuses me....... im really bad at this

Answer 21

Hold on.

Answer 22

ok

Answer 23

ooooo that makes since now thank you

Answer 24

so can i show you my work to make sure i am doing it correctly

Answer 25

i got 8x+2y=4 for the second one is that what you got?

Answer 26

i dont know what to do after this or if this is even correct...... someone please help me