Question

Solve the following systems of inequalities graphically:

$2x+y\ge 6,3x+4y\le 12$

Answer 1

The given inequality is $2x+y\ge 6$.

Draw the graph of the line 2x +y =6.

Table of values satisfying the equation

2x +y =6

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

Putting (0,0) in the given inequation, we have $2\times 0+0\ge 6\Rightarrow 0\ge 6$, which is false.

$\therefore$ Half plane of $2x+y\ge 6$is away from origin.

Also the given inequality is $3x+4y\le 12$.

Draw the graph of the line 3x+4y=12.

Table of values satisfying the equation

3x +4y =12

$\begin{array}{ccc}x& 0& 4\\ y& 3& 0\end{array}$

Putting (0,0) in the given inequation, we have $3\times 0+4\times 0\ge 12\Rightarrow 0\le 12$, which is true.

$\therefore$ Half plane of $3x+4y\ge 12$ is towards