Question

Solve the following system of equations.

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

(1, –2, –3)

(–4, –1, –2)

(–3, –2, –3)

(2, –2, –4)

Also, if anyone would like to, I was wondering if they could help me with 2 more questions that are the same.

Answer 1

I don't really get how to solve it with 3 variables know and I was wondering if anyone could help me understand it.

Answer 2

use systems of equations on two equations first...i'll choose 1 and 3 (because they're simple)

x + 4y + z = -10
x + 2y + 2z = -10

now i subtract the equations

0 + 2y - z = 0

2y = z <--take note of this..i'll use it later

i sub this value of z into the first equation

x + 4y + z = -10
x + 4y + 2y = -10
x + 6y = -10
x = -10 - 6y <---take note of this too

now i'll sub in x and z into the second equation

3x - 3y + 6z = -21

i'll simplify it first by dividing each term by 3

x - y + 2z = -7

now i substitute

(-10 - 6y) - y + 2(2y) = -7
-10 - 6y - y + 4y = -7
-3y - 10 = -7
-3y = 10 - 7
-3y = 3

y = -1

now you have a value of y...can you look for z and x now?

Answer 3

I'm sort of confused. When you added them at beginning wouldn't one of the x's have to be negative to cancel out? Also, wouldn't that be -20?

Answer 4

i didnt add..i subtracted

x - x = 0

4y - 2y = 2y

z - 2z = -z

-10 -(-10) = -10 + 10 = 0

Answer 5

Oh I didn't know that. I would always multiply one side so one of the values would cancel out. K thx.

Answer 6

well the moment i saw some single variables i knew i had to use them to make life simple hehe

Answer 7

Wouldn't x=-4 and z=2?

Answer 8

hmm...remember look at the equations i pointed for you to remember

2y = z

x = -10 - 6y

Answer 9

z=-2*

Answer 10

now that's right ^_^

Answer 11

Lol sry was a typo. DId it right but wrote it wrong

Answer 12

Tyvm lgba :)

Answer 13

my pleasure ^_^ \[\Huge \color{maroon}{\mathtt{\text{<tips hat>}}}\]

Answer 14

The following system is solved by substitution. Which expression is substituted for z in the second and third equations?

x + 5y – z = 6
3x – y – 2z = 4
3x – 2y + 3z = 13

x + 5y + 6

x + 5y – 6 <===== My answer

–x – 5y + 6

–x – 5y – 6

Am I right?

Answer 15

lol :) could you just check this real quick?

Answer 16

yup that's right

Answer 17

K thx. and lol got one more question I'll try first on my virtual quiz.

Answer 18

If I need any help, I'll post it here :)

Answer 19

well if you have a question abt it..just post as a new question..i gtg now sorry

Answer 20

K no problem, and thx for all the help :)