Question

Solve the following systems of inequalities graphically:

2x-y > 1, x -2y < -1

Answer 1

The given inequality is 2x-y > 1.

Draw the graph of the line 2x-y =1.

Table of values satisfying the equation

2x -y =1

$\begin{array}{ccc}x& 1& 2\\ y& 1& 3\end{array}$

Putting (0,0) in the given inequation, we have

$2\times 0-0>1\Rightarrow 0>1$, which is false.

$\therefore$ Half plane of 2x -y > 1 is away from origin.

Also the given inequality is x -2y < -1.

Draw the graph of the line x -2y =-1.

Table of values satisfying the equation x -2y =-1

$\begin{array}{ccc}x& 1& 3\\ y& 1& 2\end{array}$

Putting (0,0) in the given inequation, we have $0-2\times 0<-1\Rightarrow 0<-1,$ which is false

$\therefore$ Half plane of x -2y < -1 is away from origin.