Chapter 9.7, Problem 12WE

To determine

To estimate: the real solution of the systems of the nearest half unit.

Answer to Problem 12WE

The co-ordinate of the point $\left(a,b\right)$ is $\left(2.48,3.27\right)$ , $\left(c,d\right)$ is $\left(-2.48,3.27\right)$ , $\left(e,f\right)$ is $\left(0.84,-2.08\right)$ , and $\left(g,h\right)$ is $\left(-0.95,-2.08\right)$ .

Explanation of Solution

Given:

The given equation is,

  $4x^2+9y^2<36$

Calculation:

The given system of equations is:

  $\begin{array}{l}{y}^2-x^2=4\hfill \\ y=x^2-3\hfill \end{array}$

Find the solution for this system of equations to the nearest half unit.

The graph of the above system of equations is shown as below:

  

The points of intersection of the graphs of the given system of equations are the solution of the system. From the above figure, two graphs are intersecting in four different points.

Therefore, the number of real solutions of the system is four.

Find the solutions of the system.

From the graph , find the co-ordinate of the intersecting points. It is identified the points as $\left(a,b\right)$ , $\left(c,d\right)$ , $\left(e,f\right)$ and $\left(g,h\right)$ .

The co-ordinate of the point $\left(a,b\right)$ is $\left(2.48,3.27\right)$ .

The co-ordinate of the point $\left(c,d\right)$ is $\left(-2.48,3.27\right)$ .

The co-ordinate of the point $\left(e,f\right)$ is $\left(0.84,-2.08\right)$ .

The co-ordinate of the point $\left(g,h\right)$ is $\left(-0.95,-2.08\right)$ .

Conclusion:

Therefore, the co-ordinate of the point $\left(a,b\right)$ is $\left(2.48,3.27\right)$ , $\left(c,d\right)$ is $\left(-2.48,3.27\right)$ , $\left(e,f\right)$ is $\left(0.84,-2.08\right)$ , and $\left(g,h\right)$ is $\left(-0.95,-2.08\right)$ .