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^^

petri May 8, 2019

#1**+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 !!!

CPhill May 8, 2019

#2**+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 )

CPhill May 8, 2019