Chapter 9.1, Problem 17WE

To determine

To find: The solution of the nonlinear system below by studying the graphs. Check whether the estimation satisfies the equations.

Answer to Problem 17WE

The solutions of the equations is $\left(2,4\right)$ and $\left(-2,4\right)$ , they both satisfy the given equations.

Explanation of Solution

Given:

The given equations are,

  $\begin{array}{l}y=x^2\\ y=8-x^2\end{array}$

The given graph is shown in Figure 1

  

Figure 1

Calculation:

Consider the equation are,

  $\begin{array}{l}y=x^2\\ y=8-x^2\end{array}$

The two graph intersect at the points $\left(2,4\right)$ and $\left(-2,4\right)$ .

Consider the points $\left(2,4\right)$ .

  $\begin{array}{c}y={\left(2\right)}^2\\ =4\end{array}$

Also,

  $\begin{array}{c}y=8-{\left(2\right)}^2\\ =4\end{array}$

Consider the points $\left(-2,4\right)$ .

  $\begin{array}{c}y={\left(-2\right)}^2\\ =4\end{array}$

Also,

  $\begin{array}{c}y=8-{\left(-2\right)}^2\\ =4\end{array}$

The above calculation shows that the points satisfy the equations.