Represent to solution set of each of the following in equations graphically in two dimensional plane :
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,0≤6 it is not possible.
∴ we find that the point (0,0) does not satisfy the equation 3y≥6−2x.
So, the region containing the origin is represented by the given in equation as shown below: