If x2 + y2 = 21 and 2x - 2y = 2, then what is x? If there are two possible answers, then whats the larger of the 2

Question

misty1212 · Answer

hi!!

misty1212 · Answer

$$x^2+y^2=21\
2x-2y=2$$ or easier 
$$x-y=1$$ so 
$$y=x-1$$

misty1212 · Answer

you can substitute $x-1$ for $y$ in the first line and solve 
$$x^2+(x-1)^2=22$$ for $x$

misty1212 · Answer

you ok from that point on?

anonymous · Answer

can you help me through it? @misty1212

misty1212 · Answer

ok we have to go ahead and square the second term 
$$x^2+(x-1)^2=x^2=(x-1)(x-1)\
=x^2+x^2-2x+1\
2x^2-2x+1$$

anonymous · Answer

okay I got that  then what?

misty1212 · Answer

$$2x^2-2x+1=22\
2x^2-2x-21=0$$ and if you are lucky it factors

anonymous · Answer

I use the quadratic eqn right? @misty1212

misty1212 · Answer

hmm hold on usually these are cooked up to give nice answers, this one is ugly
let me see if i made a mistake

misty1212 · Answer

ooh yesssss it was 21 not 22!

anonymous · Answer

okay thank you! @misty1212

misty1212 · Answer

$$2x^2-2x+1=21\
2x^2-2x-20=0$$

misty1212 · Answer

still not that nice though 
$$x^2-x-10=0$$

anonymous · Answer

then i do quadratic eqn? @misty1212

misty1212 · Answer

yes there is no avoiding it

anonymous · Answer

what did you get for it? @misty1212

misty1212 · Answer

$$x=\frac{1\pm\sqrt{41}}{2}$$ i think