Question

Which graph shows the system 1 x² + y = 2 x² + y² = 9

Answer 1

Answer:

The graph of the system in the attached figure

Step-by-step explanation:

we have

$x^{2}+y=2$

isolate the variable y

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

This is the equation of a vertical parabola open down (because the leading coefficient is negative)

The vertex represent a maximum

the vertex is the point (0,2)

$x^{2} +y^{2}=9$ ---> equation B

This is the equation of a circle centered  at (0,0) with radius 3 units

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

using a graphing tool

The solutions are the points (-2.05,-2.19) and (2.05,-2.19)

see the attached figure