Chapter 9.4, Problem 28WE

To determine

To describe: the graph of given equation.

Answer to Problem 28WE

The graph of the system of inequalities is the shaded region which lies inside the ellipse $4x^2+9y^2=36$ .

Explanation of Solution

Given:

The given equation is,

  $4x^2+9y^2<36$

Calculation:

The boundary of the inequality $4x^2+9y^2<36$ is the graph of the equation $4x^2+9y^2=36$ an ellipse.

For the inequality $4x^2+9y^2<36$ ,

  $\begin{array}{l}\begin{array}{l}4x^2+9y^2<36\left[Theoriginalinequality\right]\\ 4\times 0^2+9\times 0^2<36\left[\text{Use }\left(\text{0,0}\right)\text{ as a test point}\right]\end{array}\hfill \\ 0<36\left[\text{True statement}\right]\hfill \end{array}$

Hence, the test point $\left(0,0\right)$ leads to a true statement in the inequality $4x^2+9y^2<36$ , so the graph of $4x^2+9y^2<36$ is the region inside the ellipse $4x^2+9y^2=36$ inclusive.

Hence, the graph of the system of inequalities is the shaded region which lies inside the ellipse $4x^2+9y^2=36$ .

  

Conclusion:

Therefore, the graph of the system of inequalities is the shaded region which lies inside the ellipse $4x^2+9y^2=36$ .