Question

ok i need help if x^2 = y^2 + 39 and x = y +3 this is a substitution method please help

Answer 1

What have you already tried ?

Answer 2

(y + 3)^2 = y^2 = 39
Y^2 + 3y + 3y +3y + 9 = y^2 + 39
That is it so far

Answer 3

check (y+3)^2 again
\((a+b)^2 =a^2+2ab+b^2\)

Answer 4

there will be only 2 "3y"s and not 3

Answer 5

could you draw out the corrected step for me please

Answer 6

(y+3)^2= y^2 + 39

y^2 +3y+3y+9 = y^2 +39

good so far ?

Answer 7

k wait

Answer 8

i have to move all of them to one side to equal 0

Answer 9

you can...but our main aim is to find 'y'
so you can move all y terms on one side and all constants(numbers) on other

Answer 10

ok so s it ok if i move both 3ys and the 9 and then subtract the y^2 and be left with 0 = 6y + 30 is that ok or no?

Answer 11

if you're moving both 3y's to other sign...means you're SUBTRACTING those 2 3y's from both sides, right ?

so wouldn't it be
0=-6y+30
?

Answer 12

oh yeah and then what cause im trying to find 2 ys

Answer 13

sry if im onfusing you

Answer 14

so
6y =30
ok ?

Answer 15

ok let me give you an example because i think im not asking the question right

Answer 16

x^2 - 4x + 4 = 0
(x- 2) (x-2)
x = 2, 2

that is what im trying to do

Answer 17

see these steps, you may get it

y^2 +3y+3y+9 = y^2 +39

y^2 -y^2 + 6y = 39-9

0 +6y = 30

y= 30/6 = ..

any doubt in any step ?

Answer 18

so if y= 5 would that be the only answer

Answer 19

find the corresponding x value

Answer 20

and yes, that x,y pair will be the only solution :)

Answer 21

ok so one of my equations is x = y + 3
x = 5 + 3
x = 8

Answer 22

yep, 8,5 is the only solution

Answer 23

now i know the first is right but the thing is i must have two ys and xs how would i get the other ones?

Answer 24

oh give me a moment

Answer 25

its not necessary to have 2 pairs of solutions

Answer 26

omg thank you so much

Answer 27

i want to cry right now

Answer 28

http://www.wolframalpha.com/input/?i=x%5E2+%3D+y%5E2+%2B+39+and+x+%3D+y+%2B3+

hyperbola : x^2 = y^2 + 39 and
line : x = y +3

meet at only one point
and hence there is only 1 solution

don't cry please :P

Answer 29

you're most welcome ^_^
since you're new here
\(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

Answer 30

is that program free?

Answer 31

thats just a website link, it won't charge you anything for its basic functionality

Answer 32

thank you i am now your fan i was gonna struggle on that one if you didn't show me

Answer 33

happy to help :)