Chapter 6.6, Problem 4LC

To determine

To state: how can we determine whether an ordered pair is a solution of a system of linear inequalities.

Explanation of Solution

Put the x-coordinate and y-coordinate of ordered pair in given system of inequalities, if they satisfy then, the given ordered pair is solution of given system of inequalities.

For example take system of inequalities such as $\begin{array}{l}y-3x\le 3\\ y+x<-2\end{array}$ .

And we have to check whether (-3, -3) is solution this system of inequalities or not.

Putting this value in inequality $y-3x\le 3$ , we get

  $\begin{array}{l}-3-3(-3)\ge 3\\ \Rightarrow -3+9\ge 3\\ \Rightarrow 6\ge 3\end{array}$

This satisfies.

Again putting (-3, -3) in inequality $y+x<-2$ we get,

  $\begin{array}{l}-3-3<-2\\ \Rightarrow -6<-2\end{array}$

This also satisfies.

Hence we can say that (-3, -3) is a solution of given system of inequalities.