Q. The no. of distinct pairs of (a, b) real numbers that would satisfy $\displaystyle x=x^3+y^4$and $\displaystyle y=2xy$.
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).
$\displaystyle \left|\begin{array}{rcl}x&=&x^3+y^4 \\y&=&2 x y\end{array}\right.$ $\displaystyle \implies$ $\displaystyle \left|\begin{array}{rcl}x(1-x^2)-y^4&=&0 \\y(1-2x)&=&0\end{array}\right.$
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 $\displaystyle x = \frac12$ must be a possible x-value. Plug in this value into the first equation and calculate the corresponding y-values.