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

Converting the in equation to equation, we obtain x + 2y = 6, i.e x + 2y -">−- 6 = 0.

Putting y = 0 and x = 0 in this equation, we obtain x = 6 and y = 3.

So, this line meets x-axis at (6,0) and y-axis at (0,3).

We plot these points and join them by a thick line. This divides the xy plane into two parts.

To determine the region represented by the given inequality, consider point O(0,0). Clearly,

$(0,0)$ does not satisfy inequality $x+2 y \geq 6$.

So, the region that does not contain the origin is represented by the given inequality.

Hence, the shaded region is the solution to the in equation.