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Heya

I need help with two questions,i thought i figured this topic out but i guess not ahahah

question 1 :
x^2-y^2=12
y=x-2
i know i have to substitute y into the first equation but from there i kind of got stuck
question 2 :
x^2+y-=25
y=x+3
again this one needs to be substituted but i kind of get confused midway whether i need to factorise it or if that's even needed for this one

thanks in advance^^

 May 8, 2019
 #1
avatar+106533 
+2

OK...first one     x^2 - y^2  = 12      and  y = x - 2

Put the secnd into the first for y  and we have

 

x^2 - ( x - 2)^2  = 12

 

x^2 - (x^2 - 4x + 4)  = 12

 

x^2 - x^2 + 4x - 4  = 12

 

4x - 4  = 12      add 4 to both sides

 

4x = 16    divide both sides by 4

 

x =  4

 

And y  =   x - 2  =   (4) - 2  =   2

 

So   (x, y)  = (4, 2)

 

EDIT TO CORRECT A PREVIOUS ERROR>>>>>thanks, heureka  !!!

 

 

 

cool cool cool

 May 8, 2019
edited by CPhill  May 9, 2019
 #2
avatar+106533 
+2

Second one      x^2 + y  =  25      y = x+3

 

Using the same idea.....

 

x^2 + (x + 3) = 25

 

x^2 + x + 3  = 25       subtract 25 from both sides

 

x^2 + x - 22 = 0         add 22 to both sides

 

x^2 + x  = 22          complete the square on x

 

x^2 + x + 1/4  = 22 + 1/4

 

(x + 1/2)^2  =  89/4   take both roots

 

x + 1/2  = ±√89 / 2      subtract 1/2 from both sides

 

x = ±√89 / 2 - 1/2

 

And y  =   x + 3  =   ±√89 / 2 - 1/2 + 3   =   ±√89 / 2 - 1/2 + 6/2  =   ±√89 / 2 + 5/2

 

So  (x , y)  =   (  ±√89 / 2 - 1/2 , ±√89 / 2 + 5/2 )

 

 

cool cool cool

 May 8, 2019

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