What is the solution of the following system of inequalities? x + y &#x2264;<!-- ≤ -->

vrotterigzl

vrotterigzl

Answered question

2022-06-21

What is the solution of the following system of inequalities?
x + y 0
x 2 + y 2 1

Answer & Explanation

Patricia Curry

Patricia Curry

Beginner2022-06-22Added 15 answers

We could describe that as the semicircular region whose center is at the origin, diameter between the points ( 2 2 , 2 2 ) and ( 2 2 , 2 2 ), in the second, third, and fourth quadrants.
We could describe it in polar coordinates
0 r 1 , 3 π 4 θ 7 π 4
There are also multiple parameterizations in two variables, the easiest one based on the polar coordinates just given.
excluderho

excluderho

Beginner2022-06-23Added 8 answers

The inequality
x 2 + y 2 1
represents all points inside and on the boundary of the unit disk.
The inequality
x + y 0
may be rewritten as
y x
which represents all points on or below the line y = x.
Putting these two together, the system represents half a disc.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?