Question

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

5. −3x + 2y ≤ 6

Answer 1

Converting the inequation to equation, we obtain $-$3x + 2y = 6, i.e $-$3x + 2y $-$ 6 = 0
Putting y = 0 and x = 0 in this equation, we obtain x = $-$2 and y = 3 respectively. So, this line meets the x-axis at ($-$2,0) and the y-axis at (0,3). We plot these points and join them by a thick line.This divides the xy plane in two parts. To determine the region represented by the given inequality, consider point O(0,0). Clearly, (0,0) satisfy the inequality $-3x+2y\le 6$. So, the region containing the origin is represented by the given inequality.
Hence, the shaded region is the solution to the inequation.