Question

Solve the following systems of inequalities graphically:

$x+2y\le 10,x+y\ge 1,x-y\le 0,x\ge 0,y\ge 0$

Answer 1

The given inequality is $x+2y\le 10$.

Draw the graph of the line x+2y =10.

Table of values satisfying the equation

x+2y =10

$\begin{array}{ccc}x& 2& 4\\ y& 4& 3\end{array}$

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

$\therefore$ Half plane of $x+2y\le 10$ is towards origin.

Also the given inequality is $x+y\ge 1$.

Draw the graph of the line x+y =1.

Table of values satisfying the equation

x+y =1

$\begin{array}{ccc}x& 0& 1\\ y& 1& 0\end{array}$

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

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

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

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

Table of values satisfying the equation

x - y =0

$\begin{array}{ccc}x& 1& 2\\ y& 1& 2\end{array}$

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

$\therefore$ Half plane of $x-y\le 0$ is away from origin.