Chapter 10, Problem 105RE

To determine

To graph: the given solution set and find the coordination of vertices and determine whether the solution is bounded or not.

Answer to Problem 105RE

  

The coordination of vertices is $x=\frac{3}{\sqrt{2}},y=\frac{3}{\sqrt{2}}$

The solution set is bounded by the graph

Explanation of Solution

Given:

  $x^2+y^2<9$

  $x+y<0$

Calculation:

We take

  $x^2+y^2<9\dots \dots \dots \dots \mathrm{..}(1)$

  $x+y<0$ $\dots \dots \dots \dots .(2)$

Equation (1) is a circle with center (0,0) and points

(3,0),(-3,0),(0,-3) and (0,3)

From equation (2), we have

  $y=-x$

This is a straight line passing through the origin

Substituting $y=-x$ into equation $(1),$ we have

  $x^2+x^2=9$

  $2x^2=9$

  $x^2=\frac{9}{2}$

  $\Rightarrow x=\pm \frac{3}{\sqrt{2}}$

  $x=\frac{3}{\sqrt{2}},y\frac{-3}{\sqrt{2}}$

  $x=\frac{3}{\sqrt{2}},y=\frac{3}{\sqrt{2}}$

These are the points where the circle and the line intersect

The solution set is bounded by the graph

  

Conclusion:

Therefore, the coordination of vertices is $x=\frac{3}{\sqrt{2}},y=\frac{3}{\sqrt{2}}$

The solution set is bounded by the graph.