Hello, juriemagic here. Normally I do not have problems with solving simultaneous equations, but this one has got me a bit. I did work it out, but still feels un-easy about the answers. Would someone please help me with this one?:
Equation 1: x^2-y^2=0
Equation 2: x^2-4x-9=4y
All and any help will be greatly appreciated!!
+118696 Hi Juriemagic,
It is good to see you again 
Equation 1: x2−y2=0
Equation 2: x2−4x−9=4y
Mmm This is an unusual one.
It always helps if you can picture what the graphs look like
x2−y2=0x2=y2y=±xThis is a big X on the number plane centred on (0,0)I can also see that the other one is a concave up parabola.anyway that meansx2−4x−9=4xorx2−4x−9=−4xx2−8x−9=0orx2−9=0(x−9)(x+1)=0or(x−3)(x+3)=0x=9orx=−1orx=3orx=−3Now I am going to check if y should be pos or neg by subbing into equ2x=981−36−9>0soy>0y=9(9,9)x=−11+4−9<0soy<0y=−1(−1,−1)x=39−12−9<0soy<0y=−3(3,−3)x=−39+12−9>0soy>0y=3(−3,3)
So the 4 points of intersection (simuiltaneous solutions) are (9,9), (-1,-1), (3,-3), and (-3,3)
Here is the graph to show you what is happening
https://www.desmos.com/calculator/lvjgdscib6
+26396 Equation 1: x^2-y^2=0
Equation 2: x^2-4x-9=4y
(1) (x-y)(x+y) = 0
(x-y) = 0 ⇒ x = y
(x+y) = 0 ⇒ x = -y
y=±x
(2) x^2 -4x-9 = 4(-x)
x^2 -9 = 0
x^2 = 9
x=±3
x^2 - 4x -9 = 4(x)
x^2 - 8x - 9 = 0 factor
(x+1)(x-9)= 0
x+1 = 0 ⇒ x=−1
x-9 = 0 ⇒ x=9
+118696 Hi Juriemagic,
It is good to see you again
Equation 1: x2−y2=0
Equation 2: x2−4x−9=4y
Mmm This is an unusual one.
It always helps if you can picture what the graphs look like
x2−y2=0x2=y2y=±xThis is a big X on the number plane centred on (0,0)I can also see that the other one is a concave up parabola.anyway that meansx2−4x−9=4xorx2−4x−9=−4xx2−8x−9=0orx2−9=0(x−9)(x+1)=0or(x−3)(x+3)=0x=9orx=−1orx=3orx=−3Now I am going to check if y should be pos or neg by subbing into equ2x=981−36−9>0soy>0y=9(9,9)x=−11+4−9<0soy<0y=−1(−1,−1)x=39−12−9<0soy<0y=−3(3,−3)x=−39+12−9>0soy>0y=3(−3,3)
So the 4 points of intersection (simuiltaneous solutions) are (9,9), (-1,-1), (3,-3), and (-3,3)
Here is the graph to show you what is happening
https://www.desmos.com/calculator/lvjgdscib6
My goodness!!!,
Melody and Heureka!!, you did it again!.. 
. It's soooo different from how I did it!. The X^2=y^2 is really what had me. Awww!, and it's really so simple!. Thank you to both of you!, you are really superb!!.
+118696 Thank you for all the flattery Juriemagic :))
You need to get used to using Desmos Graphing calculator (or any graphing calc) to help you understand what is happening with these problems.
Learning to anticipate what a wide variety of graphs will look like will help you with many problems.
I see that you are logged on at present. I hoope this means that you log on problems are over 
