Question

Solve the following systems of inequalities graphically:

$5x+4y\le 20,x\ge 1,y\ge 2$

Answer 1

The given inequality is $5x+4y\le 20$.

Draw the graph of the line 5x+4y =20.

Table of values satisfying the equation

5x +4y =20

$\begin{array}{ccc}x& 4& 0\\ y& 0& 5\end{array}$

Putting (0,0) in the given inequation, we have $5\times 0+4\times 0\le 20\Rightarrow 0\le 20$, which is true.

$\therefore$ Half plane of $5x+4y\le 20$ is towards origin.

Also the given inequality is $x\le 1$.

Draw the graph of the line x =1.

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

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

The given inequality is $y\ge 2$.

Draw the graph of the line y =2.

Putting (0,0) in the given in equation, we have $0\ge 2$, which is false.

$\therefore$ Half plane $y\ge 2$ is away from origin.