Question

solve this system of conic sections:
x^2+y^2+2x+2y=0
x^2+y^2+4x+6y+12=0

Answer 1

Subtract the second equation from the first to get


x^2+y^2+2x+2y=0
x^2+y^2+4x+6y+12=0
-------------------
0x^2 + 0y^2 - 2x - 4y - 12 = 0


So we now have the equation -2x - 4y - 12 = 0


Now solve for x to get


-2x - 4y - 12 = 0

-2x - 4y = 12

-2x = 12 + 4y

x = (12 + 4y)/(-2)

x = -6-2y

Answer 2

Now plug this into any equation. Let's pick the first one

x^2+y^2+2x+2y=0

(-6-2y)^2+y^2+2(-6-2y)+2y=0 ... plug in x = -6 - 2y

(-6-2y)(-6-2y)+y^2+2(-6-2y)+2y=0

-6(-6-2y)-2y(-6-2y)+y^2+2(-6-2y)+2y=0

36+12y+12y+4y^2+y^2-12-4y+2y=0

5y^2+22y+24=0

(y+2)(5y+12)=0

y+2 = 0 or 5y+12 = 0

y = -2 or 5y = -12

y = -2 or y = -12/5


Now use those two y values above to find the corresponding x values. Tell me what you get.

Answer 3

ok hold on while i solve

Answer 4

ok

Answer 5

ok well for when y=-2 i get x=0 or x=-2
now for when y=-12/5 i am stuck this is what is get

Answer 6

plug those y values into x = -6 - 2y

Answer 7

oh ok oops ok hold on a sec

Answer 8

ok i get x= -2 and x= -1.2

Answer 9

-1.2 = -6/5

so the two ordered pair solutions are

(-2,-2) and (-6/5,-12/5)

Answer 10

why does -1.2 = -6/5?

Answer 11

-1.2 = -(1.2)

-1.2 = -(1+ 0.2)

-1.2 = -(1+ 20/100)

-1.2 = -(100/100+ 20/100)

-1.2 = -120/100

-1.2 = -6/5

Answer 12

oh duh ok i get it lol thanks so much (: can you check two or three problems i did today to see if i did them right plz?

Answer 13

Also, if you plug in y = -12/5 and keep everything as a fraction, you get this...


x = -6-2y

x = -6-2(-12/5)

x = -6+24/5

x = -30/5+24/5

x = (-30 + 24)/5

x = -6/5

Answer 14

sure go ahead and post them