Chapter 10.8, Problem 40E

To determine

To find: solutions of the system of equations using the graphical method

Answer to Problem 40E

The solutions of the system of equations are $\left(1.19,3.59\right),\left(-1.19,3.59\right)$

Explanation of Solution

Given:

  $\{\begin{array}{c}y=e^x+e^{-x}\\ y=5-x^2\end{array}$

Calculation:

Consider the system of equations,

  $\{\begin{array}{c}y=e^x+e^{-x}\\ y=5-x^2\end{array}$

Need to sketch the graph of the equations and find the intersect points.

Enter the equations in graphing calculator as follows.

  $\begin{array}{l}{Y}_1=e^x+e^{-x}\\ Y_2=5-x^2\end{array}$

  

Set the windows as follows.

  

To get the graph of the system of equations, press GRAPH button.

  

From the display, observe that the graphs of the equations intersect in quadrant I and quadrant II.

So the number of intersect points are 2.

Round to the two decimal places set the graphing calculator as follows,

Press MODE then set FLOAT up to 2 then press ENTER.

  

To find the intersect points press $2^{\text{nd}}+\text{TRACE}$ then Press 5.

After that, use the left and right buttons to confirm the first and second curves by pressing ENTER.

  

From the display, the intersect point is $\left(1.19,3.59\right)$

Find the intersect point in the quadrant II as above.

  

From the display, the intersect point is $\left(-1.19,3.59\right)$

Therefore, the two intersect points are $\left(1.19,3.59\right),\left(-1.19,3.59\right)$

Hence, the solutions of the system of equations are $\left(1.19,3.59\right),\left(-1.19,3.59\right)$

Conclusion:

Hence, the solutions of the system of equations are $\left(1.19,3.59\right),\left(-1.19,3.59\right)$