Answer:
A) which graph represents the equation x^2 + y^2 = 2.25?
First, the general equation for a circle can be written as:
(x - a)^2 + (y - b)^2 = R^2
This is a circle of radius R centered in the point (a, b).
Then we can rewrite our equation as:
(x - 0)^2 + (y - 0)^2 = (√2.25)^2 = (1.5)^2
Then we have a circle centered at the point (0, 0) and with a radius equal to 1.5
Then we can see that the correct one is graph C.
b) Now we want to solve the system:
x^2 + y^2 = 2.25
y - x = 1
graphically.
To do it we need to graph both equations and see in which points do they intersect.
We already have the first equation graphed, so we only need to also graph the linear equation:
y - x = 1
y = 1 + x
An example of this can be seen in the graph below:
There we can estimate one of the intersections as (0.4, 1.4) and the other as (-1.4, -0.4)
