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Question

Represent to solution set of each of the following in equations graphically in two dimensional plane :

3y<6-2x


Solution

we have,

3y62x                          ...(i)

Converting the inequation into equation,we obtain,3y=6-2x

Putting x=0, we get y=63=2

Putting y=0, we get x=62=3

So, this line meets x-axis at (3,0) and y-axis at (0,2).

we plot these points and join them by a thick line. This line divides the xy-plan in two parts. To determine the region represented by the given inequality,consider the point 0(0,0).

Putting x=0,and y=0 in the in equation (i),we get,06 it is not possible.

  we find that the point (0,0) does not satisfy the equation 3y62x.

So, the region containing the origin is represented by the given in equation as shown below:

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