Question

4x^2 + 9y^2 =72

x^2 - y^2 = 5

systems of equations

Answer 1

One easy way to solve this is to perform the following steps:

Multiply both sides of the second equation by 4. Doing that will yield the following system:

4x^2 + 9y^2 = 72
4x^2 - 4y^2 = 20

Subtracting the second equation from the first yields:

13y^2 = 52

Then divide both sides by 13:
y^2 = 4

y = + or - 2

To find x, you can use substitution or you can do this:

Multiply the second equation by 9 to get this system:

4x^2 + 9y^2 = 72
9x^2 - 9y^2 = 45

Combine both equations to get:

13x^2 = 117

Divide both sides by 13 to get

x^2 = 9

x = + or - 3

Now, that yields 4 possible points:

(-3, -2), (3, -2), (-3, 2) and (3, 2)

Answer 2

@Piercethesyd

Answer 3

Will these always have 4 answers unless either x or y is 0?

Answer 4

Not always. Take the following system for example:

http://www.wolframalpha.com/input/?i=x%5E2+%2B+y%5E2+%3D+5+and+x%5E2+%2B+y%5E2+%3D+4

Answer 5

There are no intersections for that particular system.

Answer 6

Cool, like the equivalent of parallel lines in linear systems of equations.

Answer 7

lol, yes

Answer 8

It's actually called "concentric" rather than "parallel" in this case.

Answer 9

Okay, I understand. I was just drawing an equivalent, but the term is helpful.

Answer 10

As long as you're learning, that's all that matters.

Answer 11

Here's a system that yields only two solutions:

http://www.wolframalpha.com/input/?i=x%5E2+-+y%5E2+%3D+5+and+5x%5E2+%2B+6y%5E2+%3D+25