Chapter 4, Problem 26CCSR

Solution

To find: The solution of a system of equations by graphing.

The solutions set of the given system of equations are $x=-2,y=4$ and $x=2,y=0$ .

Given data:

The given system of equations is

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

Description:

The points of intersections of graphs of two equations are the common points that satisfy the given system of equations because they lie on the curves of the functions described by the given system of equations. These common points $\left(x_i,y_i\right),i=1,2,3,\dots$ are called the system of equations.

Graphs:

The graphs of equations $y=x^2-x-2$ and $y=-x+2$ are shown in Fig.1.

  

The points of intersection of two curves represented by equations of system of equations are $\left(-2,4\right)$ and $\left(2,0\right)$ .

Therefore, $x=-2,y=4$ and $x=2,y=0$ are the solutions of given system of equations.