Question

Solve the following systems of inequalities graphically:

$x+y\ge 4,2x-y>0$

Answer 1

The given inequality is $x+y\ge 4$.

Draw the graph of the line x +y =4.

Table of values satisfying the equation

x+y =4

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

Putting (0,0) in the given inequation, we have $0+0\ge 4\Rightarrow 0\ge 4$, which is false.

$\therefore$ Half plane of $x+y\ge 4$ is away from origin.

Also the given inequality is 2x-y >0.

Draw the graph of the line 2x -y =0.

Table of values satisfying the equation

2x -y =0

$\begin{array}{ccc}x& 1& 2\\ y& 2& 4\end{array}$

Putting (3,0) in the given inequation, we have $2\times 3-0>0\Rightarrow 6>0$, which is true.

$\therefore$ Half plane of 2x -y > 0 containing (3,0)