Question

What is the solution of the system of equations? (Matrix)

2x+2y+3z=-6
3x+5y+4z=3
2x+3y+4z=-10

Answer 1

@satellite73 Please assist me with this!

Answer 2

via matrix operation?

Answer 3

step by step?

Answer 4

yes to both. :D

Answer 5

Well you can solve it the easiest way which I do believe is matrix (which I suck at)

Answer 6

wait ill try

Answer 7

k :D

Answer 8

do you need the elementary row operation?

Answer 9

Not sure exactly what you mean.

Answer 10

the one you need to form it into echelon form

Answer 11

You don't need matrix

Answer 12

Elimination method is the best.

Answer 13

How would I use that on this?

Answer 14

@Azteck i think he is required to use matrix

Answer 15

No, just to solve the equation

Answer 16

then just use elimination

Answer 17

But what would be the best way to do that?

Answer 18

\[2x+2y+3z=-6[1]\]
\[3x+5y+4z=3[2]\]
\[2x+3y+4z=-10[3]\]
\[[3]-[1]\]
\[(2x+3y+4z)-(2x+2y+3z)=(-10)-(-6)\]
\[y+z=-10+6\]
\[y+z=-4[4]\]
\[[3]\times 3\]
\[3(2x+3y+4z)=3(−10)\]
\[6x+9y+12z=-30[5]\]
\[[2]\times 2\]
\[2(3x+5y+4z)=2(3)\]
\[6x+10y+8z=6[6]\]
\[[6]-[5]\]
\[(6x+10y+8z)-(6x+9y+12z)=(6)-(-30)\]
\[y-4z=6+30\]
\[y-4z=36[7]\]
\[[4]-[7]\]
\[(y+z)-(y-4z)=(-4)-(36)\]
\[5z=-40\]

Answer 19

\[z=-8\]

Answer 20

To find the y-value, substitute z into one of the equations that contain two variables (ie. [4] or [7])

Answer 21

Once you find the y-value, you can find x by subbing the two values you just found into one of the two equations in the first two lines above. (ie. [1] or [2] or [5] or [6])

Answer 22

So basically I'm spposed to have: 2x+2y+3z=-6 become 2x+2y+3(-8)=-6 and then 2x+2y+-5=-6?

Answer 23

Is this the quickest way to do it? ^^;;

Answer 24

No... There were two equations above that had two variables.

Answer 25

Find equation [4] and equation [7] above.

Answer 26

Use either one of them to find y.

Answer 27

ohh okay

Answer 28

So somethng like : y+z=-10+6 becomes y+z=-4 so -8-4=y right?

Answer 29

I suggest you copy down all the working out I gave and then read it again in your exercise book to better understand it in hard copy what I did to get z.

Answer 30

Yes.

Answer 31

No.

Answer 32

\[y+(-8)=-4\]

Answer 33

\[y-8=-4\]

Answer 34

When you move -8 to the RHS(Right Hand Side), wouldn't the negative sign change?

Answer 35

@xKingx

Answer 36

yea

Answer 37

Then why didn't you change it? Need to be careful with all your basics if you want to solve these types of questions. one mistake can cost you full marks for the question.

Answer 38

right srry, guess I'm just tired. x.x so y=4?

Answer 39

Correct.

Answer 40

Now you can use one fo the 4 equations above that had 3 variables to find x.

Answer 41

use one of*

Answer 42

So for 3(2x+3y+4z)=3(-10). We divide 3 on both sides and get (2x+3(4)+4(-8)=(-10) or rather: 2x+12-32=(-10) so 2x+-20=-10. On the right track so far? (Again I'm dead tired so brains a little slow atm)

Answer 43

Use an equation with a number beside it (ie. [?])

Answer 44

If there are brackets around a number next to an equation and the equation has three variables, use the equation. Why are you taking equations that are in the middle of being multiplied?

Answer 45

If you were tired, you would be taking advantage of that working out and finding the values quickly in order to go to bed.

Answer 46

Tired doesn't mean that you're high or drunk or anything like that.

Answer 47

Lol...? Depends on how tired you are and how many random questions of math you've had to solve for hours straight. In any case: 2x+3y+4z=-10[3]. 2x+3(4)+4(-8)=-10[3]. 2x+12-32=-10[3]. 2x+-20=-10[3]. Like that?

Answer 48

You smashed it.

Answer 49

Awesome work.

Answer 50

kewl. so x=-5 right?

Answer 51

Remember the sign changes when you move term to the other side of the equal sign.

Answer 52

when you move a term*

Answer 53

oh yeah! x.x just 5 then

Answer 54

Good job.

Answer 55

Thanks so much, ur awesome lolz.

Answer 56

No worries.