Answer:
The graph of given system of equations is shown below.
Step-by-step explanation:
Consider the given system of equations
[tex]x^2+y=2[/tex]
[tex]x^2+y^2=9[/tex]
We need to find the graph of the given system of equations.
The first equation can be rewritten as
[tex]y=-x^2+2[/tex]
It is the vertex form of a parabola [tex]y=a(x-h)^2+k[/tex] where, (h,k) is vertex and a is a constant.
In the above equation h=0 and k=2, it means vertex of the parabola is (0,2).
Leading coefficient is negative in means it is a downward parabola. The table of values is
x : -2 -1 0 1 2
y : -2 1 2 1 -2
Plot these points on a coordinate plane and connect them by a free hand curve.
The second equation can be rewritten as
[tex]x^2+y^2=3^2[/tex]
It is the standard form of a circle [tex](x-h)^2+(y-k)^2=r^2[/tex] where, (h,k) is center of the circle and r is the radius.
In the above equation h=0,k=0,r=3. So, it is a circle with radius 3 and centered at (0,0).
