Chapter 9.1, Problem 18WE

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 18WE

The solutions of the equations is $\left(1,-1\right)$ and $\left(3,3\right)$ , they both satisfy the given equations.

Explanation of Solution

Given:

The given equations are,

  $\begin{array}{l}y=x^2-2x\\ y=-x^2+6x-6\end{array}$

The given graph is shown in Figure 1

  

Figure 1

Calculation:

Consider the equation are,

  $\begin{array}{l}y=x^2-2x\\ y=-x^2+6x-6\end{array}$

The two graph intersect at the points $\left(1,-1\right)$ and $\left(3,3\right)$ .

Consider the points $\left(1,-1\right)$ .

  $\begin{array}{c}y={\left(1\right)}^2-2\left(1\right)\\ =-1\end{array}$

Also,

  $\begin{array}{c}y=-{\left(1\right)}^2+6\left(1\right)-6\\ =-1\end{array}$

Consider the points $\left(3,3\right)$ .

  $\begin{array}{c}y={\left(3\right)}^2-2\left(3\right)\\ =3\end{array}$

Also,

  $\begin{array}{c}y=-{\left(3\right)}^2+6\left(3\right)-6\\ =3\end{array}$

The above calculation shows that the points satisfy the equations.