find the solutions to the systems of nonlinear equations

Question

anonymous · Answer

|dw:1389778217447:dw|

marigirl · Answer

we can substitute y=2x into the second equation and it will look as such
$$x ^{2}+(2x)^{2}=15$$

marigirl · Answer

You will be able to solve for x now to find the x coordinate of the point of intersection..ok?

anonymous · Answer

ok

marigirl · Answer

will you be able to tell me the x coordinate you obtained?

anonymous · Answer

(x+5)(x-3) ?

marigirl · Answer

lets try again.

marigirl · Answer

$$x ^{2}+(2x)^{2}=15$$
$$x ^{2}+4x^{2}=15$$

marigirl · Answer

$$(2x )^{2} $$ means that the two has to be squared and the x too
$$(2)^{2} and (x)^{2}$$

anonymous · Answer

kay

marigirl · Answer

so now we are at 
$$5x ^{2}=15$$

anonymous · Answer

how did we get 5x

marigirl · Answer

$$x ^{2}+(2x)^{2}=15 $$
$$x ^{2}+4x ^{2}=15$$ we expanded the bracket
$$5x ^{2}=15$$ added the like terms (i.e the terms with x^2)

next step divide both sides by 5

marigirl · Answer

is that ok? are u wit me

anonymous · Answer

yes maam

anonymous · Answer

x^2= 3?

marigirl · Answer

Awesome, what can we do now? to get rid of the x squared and to get x by itself

anonymous · Answer

thank you :), and im not sure how to do that part

anonymous · Answer

whats a underoot?

marigirl · Answer

yes, so now we have 
$$x=\sqrt{3}$$
and also 
$$x=-\sqrt{3}$$

anonymous · Answer

okay got it!

marigirl · Answer

there will be a positive and a negative answer.

anonymous · Answer

so put down both?

marigirl · Answer

also at the beginning you had y=2x ( which is a straight line)
passing through a circle... therefore You MUST have two points where they cross over

anonymous · Answer

okay

marigirl · Answer

can u view my attachment

anonymous · Answer

yes,

marigirl · Answer

Your last step now is to find the y-coordinate of those two points. this can seem a little tricky because our x coordinate has a square root (I ALWAYS hated square roots)

anonymous · Answer

yeah this is hwere im really lost

marigirl · Answer

our solution are 
$$x=\sqrt{3}  $$
$$x=-\sqrt{3}$$

We now substitute this x value into any of the two original equations. I usually go for the one which looks like the easiest. to me y=2x is better to substitute in these values than the circle equation.

I will start you off. I will do $$x=-\sqrt{3}$$
y=2x
$$t=2(-\sqrt{3})$$
this can be written as
$$y=-2\sqrt{3}$$

our coordinate is
($$(-\sqrt{3}, -2 \sqrt{3})$$

marigirl · Answer

would u be able to follow what i did and come up with the second coordinate for
$$x=\sqrt{3}$$

anonymous · Answer

yeah

marigirl · Answer

what is the second coordinate you got.