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Q: Solve the following inequality graphically in two-dimensional plane: 2x + y \geq 6

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2x + y \geq 6

Graphical representation of  2x+y=6 is given in the graph below.

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

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

Let there be a  point (3,2)

We observe   6+2\geq 6    i.e. 8\geq 6  , which is true.

Therefore, half plane II  is not a solution region of given inequality i.e. 2x + y \geq 6

Also, the point on the line does satisfy the inequality.

Thus, the solution to this inequality is the half plane I, above  the line 2x+y=6  including points on this line , represented by green colour.

This can be represented as follows: 

Posted by

seema garhwal

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