Question

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

3y<6-2x

Answer 1

we have,

$3y\ge 6-2x$ ...(i)

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

Putting x=0, we get y=$\frac{6}{3}=2$

Putting y=0, we get x=$\frac{6}{2}=3$

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,$0\le 6$ it is not possible.

$\therefore$ we find that the point (0,0) does not satisfy the equation $3y\ge 6-2x$.

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