Question

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

$-3x+2y\le 6$

Answer 1

We have,

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

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

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

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

we plot these points and join them by a thick line.This line meets x-axis at (-2,0) and y-axis at (0,3).This line divides the xy-plan into 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 inequation (i),we get,$0\le 6$

Clearly,(0,0) satisfies the inequality.So the region containing the origin is represented by the given in equation as shown below.

This region represents the solution set of the given in equations.