Question

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

2. x + 2y ≥ 6 

Answer 1

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  \[x + 2y \geq 6\] 

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.