Chapter 6.6, Problem 42HP

To determine

To find: Graph of inequalities and Area of the solution .

Answer to Problem 42HP

Area of solution of inequalities = $9unit{s}^2$ .

Explanation of Solution

Given information:

  $\begin{array}{l}y\ge 1\\ y\le x+4\\ y\le -x+4\end{array}$ .

Here Violet colour represents region of inequality $y\le -x+4$

Blue colour represents region of inequality $y\ge 1$

Green colour represents region of inequality $y\le x+4$

The common region of Red colour, Green colour and Blue colour is the solution of above system of inequalities.

Here the common region contains 6 complete squares and 6 half-squares.

Area of each square is 1 $c{m}^2$ .

So Area of solution of inequalities is

Area = $6\left(1\right)+6\left(0.5\right)$

  $\Rightarrow$ Area = $6+3$

  $\Rightarrow$ Area = $9unit{s}^2$

Area of solution of inequalities is $9unit{s}^2$ .