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  • Solve the following inequality graphically in two-dimensional plane: 3x + 4y less than or equal to 12

Solve the following inequality graphically in two-dimensional plane:

    Q3.    3x + 4y \leq 12

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best_answer

3x + 4y \leq 12

Graphical representation of  3x + 4y = 12 is given in the graph below.

The line 3x + 4y = 12 divides plot into two half-planes.

Select a point (not on the line 3x + 4y = 12) 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 

                1+2\leq 12    i.e. 3\leq 12  , which is true.

Therefore, the half plane I(above the line) is not a solution region of given inequality i.e. 3x + 4y \leq 12.

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

Thus, the solution to this inequality is half plane II (below the line 3x + 4y = 12 ) including points on this line, represented by green colour.

This can be represented as follows: 

Posted by

seema garhwal

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