Question

Use the substitution method to solve
x^2+2y^2=9
x-y+3=0
can someone show me the steps?

Answer 1

I have already solved this before. You've asked the same question lol, search for the old one ^_^

Answer 2

oh wait, it's different ^^" my bad.

Answer 3

yea the y^2 is throwing me off.

Answer 4

i came up w/ x=(-1,-3) y=(2,0) but im not sure thats right...

Answer 5

Alright, first of all, call your equations as (a) and (b).

Now, let's re-write equation (b) in terms of y and we'll get:

y = 3 + x

Substitute this equation in (a) and you'll get:

\[x^2 + 2(3+x)^2 - 9 = 0\]
\[x^2 + 2(3+x)(3+x) -9 =0\]
\[x^2 + 2x^2 + 12x + 18 -9 = 0\]
\[3x^2 + 12x -9 = 0\]
\[(3x-3)(x-9) = 0\]

so x = 1 and x =3

Plug these 2 x's in equation b and find the 2 points ^_^

give it a try now :)

Answer 6

k

Answer 7

Your points should be (1,4) and (3, 6) :)

Answer 8

DOn't you mean x = 1 and x = 9

Answer 9

lol right right! >_< thank you :)

Answer 10

wait no!

Answer 11

oh dear , I messed up again the equation should be:

(3x-3)(x-3) = 0 instead of (x-9)

Answer 12

so you have x = 1 and x = 3 ^^" sorry lol

Answer 13

plug these in equation (b) and you'll get (1,4) and (3,6) as your points :)

Answer 14

and thank you blexting :)

Answer 15

it wouldnt be (1,4) and (3,12)?

Answer 16

no ,it'll be (1,4 ) and (3,6)

I made a silly mistake in the previous last line where I have put:

(3x -3)(x-9) = 0

it should be :

(3x -3)(x-3) = 0 instead :)

Answer 17

plug x = 3 in the equation and you'll get the other point (3,6)

^_^

Answer 18

ok I see. that x-9 was throwing me off. Thans for your help!

Answer 19

np :) again, sorry for the mess ^^"

Answer 20

Wait. x^2+2x+12+18-9=0
wouldnt this simplify to 3x^2+2x+9=0 ?

Answer 21

you have negative 9

Answer 22

oh right! >_< again sorry lol

Answer 23

yo'll have negative 3 and not 9

Answer 24

Ok I think i have it.

Answer 25

awesome! :)

Answer 26

awesome indeed

Answer 27

:)

Answer 28

when i solve I keep coming up with x=(-1,-3) y=(2,0)?

Answer 29

y=2 and x=1

Answer 30

or y=0 and x=3

Answer 31

yes! excellent js! :)

Answer 32

I'll give you a star ^_^

Answer 33

truly excellent...

Answer 34

a star from me too

Answer 35

lol ^_^

Answer 36

i mean y=0 and x=-3

Answer 37

lol abigail :)

Answer 38

i know what you mean, dont wory

Answer 39

thank you for your support too ^_^

Answer 40

you know what I mean?

Answer 41

i know what i know

Answer 42

so, what did I mean?

Answer 43

I know what you know I know

Answer 44

._. ...now I don't even know what I have said

Answer 45

i know you dont know what you think you dont know

Answer 46

I don't even know what I know now x_x

Answer 47

LOL, stop my head is spinning! @_@

Answer 48

Well guys i know i appreciate the help:)

Answer 49

np js :)

Answer 50

i know it is

Answer 51

I don't even know what is what right now, but I do know that the word "know" sounds funny nowx_x

Answer 52

just say "know" 29 times out loud, and then pause for 5 sec, and say it again, and i promisse, it will sound weird

Answer 53

LOL

Answer 54

go finish your 5 $ work =P

Answer 55

finished all the orders already

Answer 56

made a fortune

Answer 57

atleast you had fun :)

Answer 58

This solution was very difficult to follow. I hope js14 understands the final answer is x=-3, y=0