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Kindly answer this question without any links or hints :

Which of the following points belong to the region represented by the inequations 2x - 3y ≥ 5 and x - 2y ≤ 3 ?

1. (3,0)

2. (-4,-4)

3. (3,-5)

4. (2,-2)

5. (5,1)

$Wehave,\phantom{\rule{0ex}{0ex}}2x-3y\ge 5andx-2y\le 3\phantom{\rule{0ex}{0ex}}Putting\left(3,0\right)inbothinequations,weget\phantom{\rule{0ex}{0ex}}6\ge 5and3\le 3whichistrue.\phantom{\rule{0ex}{0ex}}Putting\left(-4,-4\right)inbothinequations,weget\phantom{\rule{0ex}{0ex}}4\ge 5and4\le 3whichisfalse.\phantom{\rule{0ex}{0ex}}Putting\left(3.-5\right)inbothinequations,weget\phantom{\rule{0ex}{0ex}}21\ge 5and13\le 3whichisfalse.\phantom{\rule{0ex}{0ex}}Similarlyput(2,-2)and(5,1).\phantom{\rule{0ex}{0ex}}AndHence\phantom{\rule{0ex}{0ex}}$

Points (3,0) and (5,1) belongs to the region represented by the inequalities $2x-3y\ge 5andx-2y\le 3$ as these both points are satisfying the inequalities.

Regards

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