Question

Use a graphical method to find estimates for the solutions of the simultaneous equations x^2 + y^2=2.25 y-x=1

Answer 1

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)