Solve the following inequality graphically in two-dimensional plane:    Q6.    $2x - 3y > 6$

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$2x - 3y > 6$

Graphical representation of  $2x - 3y = 6$ is given in the graph below.

The line $2x - 3y = 6$ divides plot in two half planes.

Select a point (not on the line $2x - 3y = 6$)which lie in one of the half-planes, to determine whether the point satisfies the inequality.

Let there be a  point $(1,2)$

We observe

$2-6> 6$    i.e. $-4 > 6$  , which is false .

Therefore, half plane I is not solution region of given inequality i.e. $2x - 3y > 6$.

Also point on line does not satisfy the inequality.

Thus, the solution to this inequality is half plane II excluding points on this line, represented by green colour.

This can be represented as follows:

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