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Solving Quadratic Systems

Ok, so I have the following system with quadratic equations:

[INDENT]X^2 + y^2 = 25
4y = 3x[/INDENT]

And I'm unsure how to go about solving it. Here's what I've tried:

[INDENT]X^2 + y^2 = 25
x^2 = 25 - y^2
x = 25 - y[/INDENT]

Which means...

[INDENT]4y = 3(25 - y)
4y = 75 - y
5y = 75
y = 15[/INDENT]

But plugging this back into the original equations doesn't seem to give me the correct result.

For example:
[INDENT]x^2 + 15^2 = 25
x^2 + 225 = 25[/INDENT]

Where am I going wrong here? It may be a really obvious answer but I really have no idea :confused:
Reply 1
Avatar for RajPopat94
RajPopat94
Okay, you're going a little bit wrong. I'd start with the second equation and make y the subject. So:

y = 3x/4

And then sub it back into the first equation:

x^2 + (3x/4)^2 = 25

x^2 + 9x/16 = 25

16x^2 + 9x = 400

16x^2 + 9x - 400 = 0

And then quadratic formularise if you can't be asked to work out factors. Get the x value and sub it back in for y :smile:
Reply 2
Avatar for pongalo
pongalo
10
if you square root one side, you need to square root the entire other side
Reply 3
Avatar for finalfanatic
finalfanatic
OP
Original post by RajPopat94
Okay, you're going a little bit wrong. I'd start with the second equation and make y the subject. So:

y = 3x/4

And then sub it back into the first equation:

x^2 + (3x/4)^2 = 25

x^2 + 9x/16 = 25

16x^2 + 9x = 400

16x^2 + 9x - 400 = 0

And then quadratic formularise if you can't be asked to work out factors. Get the x value and sub it back in for y :smile:


That made much more sense, thanks :biggrin: Although when using the quadratic formula I get a result of 4.73 or -5.29, would that be correct? I was under the impression the result should be an integer?
(edited 12 years ago)
Reply 4
Avatar for DFranklin
DFranklin
18
Original post by RajPopat94
Okay, you're going a little bit wrong. I'd start with the second equation and make y the subject. So:

y = 3x/4

And then sub it back into the first equation:

x^2 + (3x/4)^2 = 25

x^2 + 9x/16 = 25No. You mean x^2 + 9x^2/16 = 25.
Reply 5
Avatar for DFranklin
DFranklin
18
General comment to all posters. This is really only A-level work, and I'm seeing some basic algebra errors (e.g. x^2 = 25 - y^2 does NOT imply x = 25 - y) that you shouldn't even be making at A-level.
Reply 6
Avatar for finalfanatic
finalfanatic
OP
Having never done anything beyond GCSE maths this time yesterday, and only getting a B in that, I feel I've adapted pretty well to this module so far. And I will be making a few mistakes along the way, you don't learn without making mistakes.
Original post by DFranklin
General comment to all posters. This is really only A-level work, and I'm seeing some basic algebra errors (e.g. x^2 = 25 - y^2 does NOT imply x = 25 - y) that you shouldn't even be making at A-level.


Original post by finalfanatic
Having never done anything beyond GCSE maths this time yesterday, and only getting a B in that, I feel I've adapted pretty well to this module so far. And I will be making a few mistakes along the way, you don't learn without making mistakes.


I presume therefore that you're at university, but not studying a very maths-heavy degree? I would suggest labelling your posts as A-level standard until you start doing some things which are significantly more difficult - the post labels should refer to the "maths level" that you are operating at, rather than your own personal situation. Of course, we understand that having not taken maths beyond GCSE you might not know what constitutes A-level and what would be undergraduate standard! For your information, this kind of thing is definitely beginning-of-AS-level or GCSE standard, so you probably won't be heading into undergraduate territory for a while. Save the undergraduate label for post-A-level maths work.
Reply 8
Avatar for Dog4444
Dog4444
10
Also, this might be interesting for someone: http://en.wikipedia.org/wiki/Pythagorean_triple

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