Question

Solve the following systems of inequalities graphically:

$3x+2y\le 150,x+4y\le 80,x\le 15,y\ge 0,x\ge 0$

Answer 1

The given inequality is $3x+2y\le 150$.

Draw the graph of line 3x+2y =150.

Table of values satisfying the equation

3x+2y =150

$\begin{array}{ccc}x& 30& 40\\ y& 30& 15\end{array}$

Putting (0,0) in the given inequation, we have $3\times 0+2\times 0\le 150\Rightarrow 0\le 150$, which is true.

$\therefore$ Half plane of $3x+2y\le 150$ is towards origin.

Also the given inequality is $x+4y\le 80$.

Draw the graph of the line x +4y =80.

Table of values satisfying the equation

$\begin{array}{ccc}x& 0& 40\\ y& 20& 10\end{array}$

Putting (0,0) in the given inequation, we have $0+4\times 0\le 80\Rightarrow 0\le 80$, which is true.

$\therefore$ Half plane of $x+4y\le 80$ is towards origin.

The given inequality is $x\le 15$.

Draw the graph of the line x =15.

Putting (0,0) in the given inequation, we have $0\le 15$, which is true.

$\therefore$ Half plane of $x\le 15$ is towards origin.