Question

Solve by the method of your choice.
x^3 + y = 0
11x^2 - y = 0

Answer 1

Why not start by adding?

Answer 2

so then you end up with
x^3 + 11x^2 = 0
right

Answer 3

So x is definitely a solution, but if you factor, you get something weird. Hmm.

Answer 4

x = 3

Answer 5

Can't type, I mean x =0

Answer 6

so then y = 0

Answer 7

Yes, but if you factor this thing, what do you get?

Answer 8

I factor
x^3 + 11x^2 = 0
right

Answer 9

If you factor out x^2, what is the answer you get by letting the other term = 0.

Answer 10

-11

Answer 11

Yes, so plug into one of the equations and solve for y.

Answer 12

-1331

Answer 13

oops it is 1331

Answer 14

1 0 1 | 0
0 11 -1 | 0

and rref to define the nulspace

Answer 15

Stick with me.

Answer 16

x = -11 , y = 1331
does that solve eqn 2?

Answer 17

yes

Answer 18

Great.

Answer 19

it makes them both 0

Answer 20

so there is two solutions
(0,0)(-11, 1331)

Answer 21

yes

Answer 22

thank you

Answer 23

I think I know what I am doing I just confuse myself sometimes

Answer 24

I think the other answer was just misguided. Keep it simple.