Question

How would I go about solving this? I'm lost?


Solve the following system of equations.

x + 4y + z = –10
3x – 3y + 6z = –21
x + 2y + 2z = –10

Answer 1

linear algebra?

Answer 2

System of equations with three variables.

Answer 3

z = -10 -x -4y <---- eq1.

Answer 4

3x -3y +6( -10 -x -4y) = -10

Answer 5

-3 x-27 y-50 = 0

Answer 6

same as with second one, eliminate "z" from the 3rd equation as well.

Answer 7

let me try and illl post my trials...

Answer 8

If I remember correctly you can apply the Gram Schmit process and come up with the same

Answer 9

x + 2y + 2z = –10

x + 2y + 2(-10 -x -4y) = –10

-x-6 y = 10

Answer 10

now, we have:

-3x-27y-50 = 0
-x - 6y = 10

Answer 11

Solve for x and y.

Answer 12

(1, –2, –3)
(–4, –1, –2)
(2, –2, –4)
(–3, –2, –3)

those are my answers

Answer 13

possible answers btw

Answer 14

B

Answer 15

okay, but how do i get b?

Answer 16

Calc. ;)

Answer 17

im trying to figure it out..

Answer 18

but i have to show my work :O

Answer 19

thanks :)

Answer 20

im doing it in my book, wait please.

Answer 21

Got it. xD

Answer 22

x + 4y + z = –10
3x – 3y + 6z = –21
x + 2y + 2z = –10

Solving eq 1 for z:

z = -10 - x -4y

Now, subsitute this value in both eq 2 and eq 3


3x – 3y + 6z = –21 & x + 2y + 2z = –10
3x -3y + 6(-10 - x -4y) = -21 x + 2y +2(-10 - x -4y) = -10
Solve and you will get; Solve and you will get;
-3x - 27y = 39 -x -6y = 10

Answer 23

now solve these two for x and y.
so x = -4, y = -1

as now you have both, solve them in any equation for z.

And you are done!! :)

Answer 24

Here's how people do it using linear algebra. It tends to get to the right answer without to much confusion.