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Question


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

3x+2y6

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Solution

We have,

3x+2y6 ...(i)

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

Putting x=0,we get y=62=3

Putting y=0,we get y=63=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,06

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.


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