Question

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

10. 3x − 2y ≤ x + y − 8

Answer 1

Converting the inequation to equation, we obtain 3x $-$ 2y $-$ x $-$ y + 8 = 0, i.e 2x $-$ 3y + 8= 0
Putting y =0 and x = 0 in this equation, we obtain x = $-$ 4 and y = 8/3 respectively.
So, this line meets the x-axis at ($-$4, 0) and y-axis at (0,8/3).
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 the inequality.
So, the region that does not contain the origin is represented by the given inequality.
Hence, the shaded region is the solution to the inequation.