Find the Coordinates of the points of intersection for the graphs of x^2+2y^2=33 and x^2+y^2=2+19

Question

misty1212 · Answer

HI!!

misty1212 · Answer

set them equal, solve for $x$

misty1212 · Answer

$$x^2+2y^2=33\
x^2+y^2=21$$ like that?

misty1212 · Answer

the $2+19$ is a little confusing 
is that really what it says?

anonymous · Answer

2x+19 sorry!!!

misty1212 · Answer

oh that sucks 
we can still do it

misty1212 · Answer

$$x^2+2y^2=33\
x^2+y^2=2x+19$$

misty1212 · Answer

i don't know of a quick way to do it 
if you subtract the second equation from the first you get $$y^2=-2x+14$$

misty1212 · Answer

then you can substitute that in to either equation to get an equation with only $x$

anonymous · Answer

I am doing test corrections so I already know the answer needs to be  (5, +-2) (-1,4). I just need help on the work. If having the answer helps at all

misty1212 · Answer

for example here $$x^2+2y^2=33\x^2+2(-2x+14)=33$$

misty1212 · Answer

yeah i know the answer, used wolfram already 
just trying to figure out how to do it is all 
in any case once you have $$x^2+2(-2x+14)=33$$ it is a quadratic equation with only $x$ and you will get two x values
do you know how to solve it?

anonymous · Answer

no clue

misty1212 · Answer

lol multiply out first on the left $$x^2-4x-28=33$$

misty1212 · Answer

oops $$x^2-4x+28=33$$ thats better

misty1212 · Answer

subtract $33$ from both sides get $$x^2-4x-5=0$$ then factor

anonymous · Answer

im trying to get x right?

misty1212 · Answer

yes, you have to factor it first  
you know what i mean?

anonymous · Answer

like get to 4x=x^2-5 ?

misty1212 · Answer

oh no

misty1212 · Answer

like $$x^2-x-6=(x-3)(x+2)$$ like that factoring

misty1212 · Answer

you know how to factor?

anonymous · Answer

It has been awhile.

misty1212 · Answer

think of two numbers that multiply to get $-5$ and add to get $-4$
hint, you have almost no choices

anonymous · Answer

5 and -1

misty1212 · Answer

close 
they multiply to get $-5$ but if you add $5+(-1)$you get $4$ and you want $-4$

misty1212 · Answer

just change the signs

anonymous · Answer

-5 and 1

misty1212 · Answer

right, so $$x^2-4x-5=(x-4)(x+1)$$

misty1212 · Answer

solve $$(x-5)(x+1)=0$$ by solving $$x-5=0$$ and $$x+1=0$$ 
those will give the two answers you knew you were supposed to get

anonymous · Answer

so do i do the same thing with y now