Question

Solve the following systems of inequalities graphically:

$x-2y\le 3,3x+4y\ge 12,x\ge 0,y\ge 1$

Answer 1

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

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

Table of values satisfying the equation

x-2y =3

$\begin{array}{ccc}x& 1& 5\\ y& -1& 1\end{array}$

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

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

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

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

Table of values satisfying the equation

3x +4y =12

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

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

$\therefore$ Half plane of $3x+4y\ge 12$ is away from origin.

The given inequality is $y\ge 1$.

Draw the graph of the line y =1.

Putting (0,0) in the given inequation, we have $0\ge 1$, which is false.

$\therefore$ Half plane of $y\ge 1$ is away from origin.