Question

Solve the following systems of inequalities graphically:

$4x+3y\le 60,y\ge 2x,x\ge 3,x,y\ge 0$

Answer 1

The given inequality is $4x+3y\le 60$.

Draw the graph of the line 4x +3y =60.

Table of values satisfying the equation

4x +3y =60

$\begin{array}{ccc}x& 15& 0\\ y& 0& 20\end{array}$

Putting (0,0) in the given inequation, we have $4\times 0+3\times 0\le 60\Rightarrow 0\le 60$, which is true.

$\therefore$ Half plane of $4x+3y\le 60$ is toawards origin.

Also the given inequality is $2x-y\le 0$.

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

Table of values satisfying the equation

2x - y =0

$\begin{array}{ccc}x& 5& 10\\ y& 10& 20\end{array}$

Putting (10,0) in the given inequation, we have $2\times 10-0\le 0\Rightarrow 20\le 0$, which is false.

$\therefore$ Half plane of $2x-y\le 0$ does not contain (10,0).

The given inequality is $x\ge 3$.

Draw the graph of the line x =3.

Putting (0,0) in the given inequation, we have $0\ge 3$, which is false.

$\therefore$ Half plane of $x\ge 3$ is away from origin.