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So do this: y = 12/x
Now plug this in the second equation.

How do I plug this in?
Like, x^2 + 12/x = 40?

\[x^2 + y^2=40\]
\[x^2+(12/x)^2 = 40\]
\[x^2 + \frac{144}{x^2} = 40\]

Then multiply everything by \(x^2\) to get rid of the fraction and solve.

I'm confused

Why don't you tell me what part of that makes sense to you, and what part doesn't?

Everything is a big ball of confusion, I don't get why anything of this not coming through to me

Ok, I think I'm with you so far...

Did you understand how I solved the equation by factoring?

Kinda, except how the 36 & 4 came in

Ah nevermind, 4 * 36 = 144, that was the factored out version of 144 right?

Well, what are the factors of 144?
1*144
2*72
3*48
4*36
6*24
8*18
12*12

Got it but why 4 * 36?

Got that,

Ok, so a=36, b= 4, a*b= 144, is what your saying right?

If its zero then wouldnt it make all the answers 0?

Please, no laughing, this is serious stuff ;-)

Oh no I'm not laughing lol.
So I dont use the x^2 to find the answers?

Ah, sorry, my solutions are (6,2) and (-6,-2)

Would it be (2,3) & (-2, -3) ?

I agree with the x values, but I'm not so sure about the y values. How did you get them?

I divided 12 by 4,

Why 4? 4 isn't the value you found for x...

Should I of done it by 2?

Yes.

So then it should be (2,6) & (-2, -6)

Right. Notice the symmetry with my solutions? There's a reason for that! Here's a picture:

Ah

I think I'm still shaky with the substitution method, I could use another problem :P

Okay, I'll give this one a try,

It might look more complicated, but I think it is a bit easier...

"now plug that in ..." is the substitution process we're practicing...

How would I plug that in the x's place?
(10-5) ^2 + 4y^2 = 100?

You just lost me...

\[x+y= 10 \implies x = 10-y\]Right?

(the arrow means "implies")

Yes,

yes, you would solve it? I'm happy to hear that :-)

Yes as in reply to, " x+y=10⟹x=10−y
Right?"
lol

Alrighty, take your time.
It'll take a bit to get use to these problems

Everything makes sense up to step 4 where the 10 was taken out,
How/why was it taken out?

10-y-5 = 10-5-y = 5-y, no?

*face palm* Got it lol

25y^2?

no...take another look.

5*5= 25,
2 -'s = +
2 y's = y^2
I thought?

\[(a-b)(a-b) = a(a-b) - b(a-b) = a^2 - ab - ba + b^2 = a^2 -2ab + b^2\]

You are thinking of \[(a+b)(a-b) = a^2-ba + ba - b^2 = a^2-b^2\]I think...

Who knows what I was thinking...

Yikes & yuck aha.
Hopefully you had some tomato juice on hand

^thats an easier way way to understand it, having it step by step by step