Question

What is the maximum number of possible solutions for the system shown below?

Answer 1

Answer:

The system has no solution

Step-by-step explanation:

we have

$3x^{2} +y^{2}=4$ ------> equation A

$x^{2} +y=5$ -----> equation B

we know that

The solution of the system of equations is the intersection points both graphs

Using a graphing tool

see the attached figure

The figure has no point of intersection

therefore

The system has no solutions

Answer 2

The first function $3x^2 +y^2 = 4$ describes an ellipse.
The 2nd function $x^2 +y =5$ describes a parabola.

If you draw an ellipse and then draw a parabola where vertex is centered and above ellipse, you will see that it intercepts the ellipse twice on either side.

Maximum number of solutions = 4