Question

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

3x^2+y^2=4
x^2+y=5

choices
1
2
3
4

Answer 1

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

Answer 2

The system has no solution

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