Needing help in this question

Q. The no. of distinct pairs of (a, b) real numbers that would satisfy $x=x^3+y^4$ and $y=2xy$ .
A-5
B-12
C-3
D-7

dont laugh anyone on such elementary question....help!!

Quote:

Originally Posted by findmehere.genius

Q. The no. of distinct pairs of (a, b) real numbers that would satisfy $x=x^3+y^4$ and $y=2xy$ .
A-5
B-12
C-3
D-7

dont laugh anyone on such elementary question....help!!

I've found 5 pairs of real numbers (and 2 pairs of complex numbers).

$\left|\begin{array}{rcl}x&=&x^3+y^4 \\y&=&2 x y\end{array}\right.$ $\implies$ $\left|\begin{array}{rcl}x(1-x^2)-y^4&=&0 \\y(1-2x)&=&0\end{array}\right.$

All results containing y = 0 satisfy the second equation. From the first equation you'll get 3 different values of x if y = 0.

From the second equation you find out that $x = \frac12$ must be a possible x-value. Plug in this value into the first equation and calculate the corresponding y-values.

Thanks for the answer...now some paperwork needed to get them into head.