Can you help me with this problem?

Question

Find the points of intersection of the graphs of x^2/9 + y^2/16 =1 and x^2/9 - y^2/16 =1.

Can you show me how you would even begin to solve this? I know the answer has to be the point that satisfies both equations but I dont know how I would isolate a variable in one of the equations to substitue if that is even how your suposed to solve it.

Thanks in advance.

Answer 1

You do this: you add the two equations and you get 2*x^2/9=2
then x^2=9=>x=+3 and x=-3.
Then you substitute these values in either one of the equations and get the values for y.
Which is one value: y=0;
so your graphs have two intersection points: (-3,0) and (3,0).

Answer 2

One is an ellipse and another is a hyperbola( both are conic sections)

Add the two equations

x²/9 + y^2/16 + x²/9 - y²/16 = 1 + 1

2*x²/9 = 2

x²/9 = 1

x² = 9

x = +3,-3

Put x= 3 in first equation:

3²/9 + y²/16 =1

1 + y²/16 =1

y² = 16

y = +4,-4

Put x = -3 in the first equation :

you get
y = +4,-4

Thus there are four points of intersection:
(3,4),(3,-4),(-3,4) amd(-3,-4)