Question

use substition to find x and y

(a) x-y=-8
(b) x^2-y=-2

Answer 1

Hi

Answer 2

So these equations must go together, what would you like to solve for x or y is doesn't matter which one we do

Answer 3

Do you know how to solve for x or y?

Answer 4

yeah I know how to solve, I was just wondering how to get rid of the x^2 on the second equation

Answer 5

I rearranged the first equation so it looked lie x=-y-8, then I plugged it into the second equation

Answer 6

You don't have to really red rid of it if these are a system of equations

Answer 7

Or are these separate?

Answer 8

(-y-8)^2 -y=-2 This is what I end up with

Answer 9

You have to use the foil method because remember that (-y-8)^2 means (-y-8)(-y-8)

Answer 10

If something is squared like that it will always be the inside times the inside

Answer 11

Does this make sense?

Answer 12

so it will end up looking like y^2 +8y+8y+64-y=-2

Answer 13

Just a second

Answer 14

I caught something when you moved the y to the other side

Answer 15

It's suppose to be a + not a -

Answer 16

You have to do the opposite so it's subracting y in the original equation so your going to have to add by y so it will be a positive sign

Answer 17

Yes

Answer 18

y^2 +8y+8y+64+y=-2
then combine like terms and you get y^2+17y =-66 (is this right)

Answer 19

Yes

Answer 20

ok, this is where I got

Answer 21

I would keep the 66 on the other side though so you can factor

Answer 22

...stuck (sorry hit enter)

Answer 23

would 11 and 6 work

Answer 24

yes

Answer 25

So than y would equal?

Answer 26

would y have two answers

Answer 27

Yes but 11 and 6 aren't it because you have (y+11)(y+6)=0

Answer 28

I know we would have to set both of those factors = 0 so it's actually -11 and -6

Answer 29

Yes good

Answer 30

ok, so which one do we use to plug back into our equation to get x

Answer 31

It doesn't matter they would both be the same answers but since the first one is easiest I would you the first equation

Answer 32

so if I were to graph this, there should be two spots on the graphs where they touch because we have two sets of ordered pairs right

Answer 33

Hmmmmmmmm

Answer 34

just checked it! And it does have two points

Answer 35

Omg I'm sorry I missed something again It would be easier If I would have done this on paper x=y-8 so you will have a -16y not positive I am so sorry

Answer 36

Because that that would be (y-8)^2 y^2-16x+64-y+2=0

Answer 37

So y^2-17y+66=0

Answer 38

that's okay, I figured that out as well

Answer 39

I don't know why I missed two errors but now you would just get positive y values not negative and than get your corresponding x values

Answer 40

So we were close the first time

Answer 41

Does that make sense?

Answer 42

yep, I figured that out, as soon as I graphed the two equations! Thanks for the help

Answer 43

No problem :)