Answer
No solution
Work Step by Step
Step 1. Multiply the second equation by $y$.
$x^2y=16$
$x^2y+4y^2+16y=0$
Step 2. Substitute the first equation to the second one and then solve for $y$.
$16+4y^2+16y=0$ Divide by $4$
$y^2+4y+4=0$
$(y+2)^2=0$
$y=-2$
Step 3. Solve for $x$.
$x^2\cdot (-2)=16$
$x^2=-8$
Since $x^2\geq 0$, the last equation has no solution.
Step 4. Conclude the solution.
The nonlinear system has no solution.
