Question

Solve.
x+4y+z=-10
3x-3y+6z=-21
x+2y+2z=-10

Answer 1

do you know how to convert this to matrix and solve with matrix algebra?

Answer 2

I ave to use substitution and elimination .

Answer 3

have*

Answer 4

google those then :) i was thinking substitution but that will take a while.

Answer 5

how do i do it ?

Answer 6

I'll give you definitions. Subs method is solving for one variable in one equation and plugging into the other equations.

Answer 7

http://www.purplemath.com/modules/systlin5.htm Here is eliminations I guess they multiply to eliminate constants and variable.s

Answer 8

HINT: first and third equations give you opportunity to easily eliminate x

Answer 9

HINT: then use the first and second equations to eliminate x again.

The resulting two equations with x eliminated can both be solved for y and z. Then, easy as usual, you can just plug y and z back in to get x.

Answer 10

Try doing it a bit yourself, and I will help you if you need further help :)

Answer 11

So elimination? and then which one do i solve for?

Answer 12

Okay. When you see this kind of system, the first goal is to simplify it. We do this by eliminating variables. That makes sense right?

Answer 13

x+4y+z=-10 call this equation 1 (I will use e1 for short)
3x-3y+6z=-21 call this equation 2 (I will use e2 for short)
x+2y+2z=-10 call this equation 3 (I will use e3)

Answer 14

by combining different equations, we can get simplified results.

Answer 15

which ones should i combine first ?

Answer 16

Btw, combining does not mean adding. You can combine any multiple of the entire equation (remember that means negatives included)

Answer 17

huuhhhhhhh ?

Answer 18

Okay. I'll worth through a little bit of this problem, but you might have to give me 5 mins, cause I have to do some stuff and I'm also helping someone else with long division.

Answer 19

Subtract equation 3 from equation 1.
In other words,
x+4y+z-(x+2y+2z)=-10-(-10)
Does this make sense?

Answer 20

not really):

Answer 21

Okay. What didn't make sense?

Answer 22

subtracting it ?

Answer 23

Okay. I'll do it another way.
x+4y+z=-10 is e1 (equation one) right?

Answer 24

x+2y+2z=-10 is equation 3 right?

Answer 25

is the answer .. (1,-2,-3) ?

Answer 26

How'd you get that :)

Answer 27

I took the answers and put them in until i got -10 = -10 hahaha

Answer 28

x = -4, y = -1, z = -2

Answer 29

is that correct??

Answer 30

mines is :P

Answer 31

plug them in and see if they work.