Question

Solve the following systems of inequalities graphically:

$2x+y\ge 4,x+y\le 3,2x-3y\le 6$

Answer 1

The given inequality is $2x+y\ge 4$.

Draw the graph of the line 2x +y =4.

Table of values satisfying the equation

2x+y =4

$\begin{array}{ccc}x& 2& 1\\ y& 0& 2\end{array}$

Putting (0,0) in the given inequation, we have $2\times 0+0\ge 0\Rightarrow 0\ge 4$, which is false.

$\therefore$ Half plane of $2x+y\ge 4$ is away form origin.

Also the given inequality is $x+y\le 3$.

Draw the graph of the line x +y =3. Table of values satisfying the equation

x+y =3

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

Putting (0,0) in the given inequation, we have $0+0\le 3\Rightarrow 0\le 3$, which is true.

$\therefore$ Half plane of $x+y\le 3$ is towards origin.

The given inequality is $2x-3y\le 6$.

Draw the graph of the line 2x -3y =6.

Table of values satisfying the equation

2x-3y =6

$\begin{array}{ccc}x& 0& 3\\ y& -2& 0\end{array}$

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

$\therefore$ Half plane of $2x-3y\le 6$ is towards origin