Question

Please help with these 2 problems! Will give medal to best answer!

Please show steps.

1. Solve the system by elimination.
-2x+2y+3z=0
-2x-y+z=-3
2x-3y+3z=5

2. Solve the system by substitution.
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

Answer 1

@jim_thompson5910 can you help?

Answer 2

@hartnn @thomaster

Answer 3

how far did you get?

Answer 4

I tried on the first one and ended up erasing it because I didn't think it was right. It didn't make sense. I got 2x-5y+6z=-2 I think.

Answer 5

do you know how elimination works?

don't worry about equations with 3 variables

I'm asking just for 2 variable systems right now

Answer 6

Not really.

Answer 7

ok then go ahead and read this page to get more familiar with the concept of elimination

http://www.purplemath.com/modules/systlin5.htm

I recommend you practice the equations with 2 variables first before you move up to the 3 variable equations

Answer 8

Okay thanks.

Answer 9

np, let me know if that page helps or not

Answer 10

That is the page I looked at before I made this post. I feel like all her equations are put together really well with the same or similar terms right on top of each other. It doesn't really help me much

Answer 11

@jonnymiller

Answer 12

hmm alright, I was afraid of that, let's see how far we get with this

Answer 13

let's focus on the first two equations

-2x+2y+3z=0
-2x-y+z=-3

and let's say we want to get rid (or eliminate) the y terms

we could add up +2y and -y to get 2y + (-y) = 1y = y

but that's NOT 0y or 0 like we want

Answer 14

to fix this we can turn that -y into -2y

notice now that

2y + (-2y) = 0y = 0

so the y terms have gone away

Answer 15

so basically you double everything in equation 2, then add


double everything in equation 2 to get

-2x-y+z=-3

-4x-2y+2z=-6



then add the equations to get

-2x+2y+3z=0
-4x-2y+2z=-6
--------------
-6x+0y+5z = -6


that turns into

-6x + 5z = -6


with me so far?

Answer 16

Yeah I think so.

Answer 17

But why isn't the first equation doubled too?

Answer 18

because we have 2y in the first equation

we have -y in the second equation

we want these two expressions to have equal (yet opposite) coefficients so they add to 0

Answer 19

so we have -y....but we want -2y

so we have to double -y to get -2y

you have to do this with every term in the equation where -y is (the second equation) to make sure everything is balanced

Answer 20

hopefully that's clearer

Answer 21

Oh okay. Yeah I think I get it.

Answer 22

now let's focus on the 2nd and 3rd equations

-2x-y+z=-3
2x-3y+3z=5

Answer 23

in it's current form, if we add -y to -3y, we get

-y + (-3y) = -4y

that's not 0y like we want, so we have to adjust the -y into +3y to make sure that the two 'y' terms add to 0y

-------------------------------------------

so you have to multiply everything in equation 2 by -3 to get

-2x-y+z=-3

6x+3y-3z=9

--------------------------------------------

now add this to equation 3


6x+3y-3z=9
2x-3y+3z=5
------------
8x+0y+0z=14

that turns into

8x = 14

Answer 24

what's next?

Answer 25

Divide both sides by 8?..

Answer 26

correct

Answer 27

so x = ???

Answer 28

1.75

Answer 29

good, or x = 7/4 as a fraction

Answer 30

now use this value of x to find y and z

Answer 31

I got -3.5+2y+3z=0. For the next step do I subtract 3z from both sides?

Answer 32

pick on an equation that only has x and y

or that has x and z

Answer 33

then plug in x = 1.75 or x = 7/4

then solve for the remaining variable

Answer 34

for my x value I got x=(5/2)

I solved for x y and z and my values check out when I plug them back in.

Answer 35

I'm confused now..

Answer 36

no it should be x = 7/4 or x = 1.75

Answer 37

x = 5/2 is incorrect

Answer 38

So do I use the -6x+5z=-6?

Answer 39

yes, plug x = 1.75 or x =7/4 into that equation

then solve for z

Answer 40

yes you are right....my solutions work for the first 2 equations but not for the 3rd

Answer 41

I got z=-1.09

Answer 42

that is incorrect

Answer 43

-6x+5z=-6

-6(1.75)+5z=-6

-10.5+5z=-6

5z = -6 + 10.5

5z = 4.5

z = ???

Answer 44

@jim_thompson5910 sorry it took so long. had to run somewhere.
z=0.9?

Answer 45

Now do I plug that in for z and solve for y?

Answer 46

yes and if you need to you can plug in for both x and z to solve for y.
but only do that if you absolutely have to

Answer 47

so x=4?

Answer 48

@killerdime20

Answer 49

you found that x = 1.75

not sure how you got x = 4

Answer 50

but yes z = 0.9

Answer 51

Which equation do I use to find y?

Answer 52

use the first one. it will be the easiest since it is set equal to 0

Answer 53

you know that x = 1.75 and z = 0.9

you now can go to any equation you want that has a y in it

Answer 54

plug those values in, then solve for y

Answer 55

1.2=y?

Answer 56

not quite