If you have y^2+x^2=40,000 , can you square root the entire side of each equation, so you'd end up with y+x= sqrt (40,000)? If not, how would I solve this equation?

Question

anonymous · Answer

wrong if you do  y+x= sqrt (40,000

anonymous · Answer

there is infinity solutions

anonymous · Answer

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anonymous · Answer

Thanks everyone for the answers! However, I'm still a little confused. In the question, I have to find out where two equations cross; in this case, the equation i just mentioned is one of them and I wanted to get it in slope intercept form. So... are you saying that I could simplify the equation in the way I mentioned; I just couldn't solve for it because there is an infinite number of answers?

anonymous · Answer

can you write both the equations ?

anonymous · Answer

y=2x+4
and
y^2+x^2=40,000

anonymous · Answer

simply plug y=2x+4 and solve for x
(2x+4)^2+x^2=40000
find x and then y from first equation.

anonymous · Answer

Got it. Thanks! Also, one last quick little clarification for the future so I don't confuse myself: if I had x^2+y^2=40,000, and I just wanted to simplify it, I could square root both sides? I wasn't sure if you were allowed to because it's addition.

anonymous · Answer

$$4x^2+16x+16+x^2=40,000$$
$$5x^2+16x-39984=0$$
$$x=\frac{ -16\pm \sqrt{256-4*5*-39984} }{ 2*5 }=\frac{ -16\pm \sqrt{256+799680} }{10 }$$
$$=\frac{ -16\pm \sqrt{799936} }{ 10 }=?$$

anonymous · Answer

$$\sqrt{x^2+y^2+2xy}=x+y$$
or $$\left( x+y \right)^2=x^2+y^2+2xy$$

anonymous · Answer

Okay, got it. Thank you so much for helping!