Chapter 9.9, Problem 3ST

(a)

To determine

To graph: the givne equations.

Answer to Problem 3ST

  

Explanation of Solution

Given:

  $9y^2+16x^2=144$

  $x^2+y^2=9$

Calculation:

Since the given system consists of a linear and a quadratic equation, it is a quadratic system. The real solutions of such a system can be determined by finding the points at which the individual quadratic graphs intersect.

Let us graph the two given equations on the same co-ordinate plane, and find the number of points at which they intersect.

  

Conclusion:

The equations are graphed.

(b)

To determine

The number of real solutions.

Answer to Problem 3ST

The system of equations has two real solutions.

Explanation of Solution

Given:

  $9y^2+16x^2=144$

  $x^2+y^2=9$

Calculation:

From the graph, it can be seen that the graphs intersect at two points.

So, the system of equations has $2$ real solutions.

Conclusion:

The system of equations has two real solutions.

(c)

To determine

To estimate: The real solution to the nearest half-unit.

Answer to Problem 3ST

The two real solutions for the given system are $(-3,0)and(3,0)$

Explanation of Solution

Given:

  $9y^2+16x^2=144$

  $x^2+y^2=9$

Calculation:

The two points where the graphs intersect are $(-3,0)and(3,0)$

Therefore, the two real solutions for the given system are $(-3,0)and(3,0)$

Conclusion:

The two real solutions for the given system are $(-3,0)and(3,0)$