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Question

Solve the following systems of inequalities graphically:

x2y3,3x+4y12,x0,y1

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Solution

The given inequality is x2y3.

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

Table of values satisfying the equation

x-2y =3

x15y11

Putting (0,0) in the given inequation, we have 02×0303,which is true.

Half plane of x2y3 is towards origin.

Also the given inequality is 3x+4y12.

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

Table of values satisfying the equation

3x +4y =12

x40y03

Putting (0,0) in the given inequation, we have 3×0+4×012012, which is false.

Half plane of 3x+4y12 is away from origin.

The given inequality is y1.

Draw the graph of the line y =1.

Putting (0,0) in the given inequation, we have 01, which is false.

Half plane of y1 is away from origin.


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