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  • Solve the following inequality graphically in two-dimensional plane: x + y < 5

Solve the following inequality graphically in a two-dimensional plane: 

    Q1.    x + y < 5

Answers (1)

best_answer

The graphical representation of  $x+y=5$ is given in the graph below.

The line $x+y=5$ divides the plot into two half-planes.

Select a point (not on the line $x+y=5$) that lie in one of the half planes, to determine whether the point satisfies the inequality.

Let there be a  point $(1,2)$

We observe 

$1+2<5$    i.e. $3<5$  , which is true.

Therefore, half-plane (above the line) is not a solution region of given inequality i.e. $x+y<5$.

Also, the point on the line does not satisfy the inequality.

Thus, the solution to this inequality is half-plane below the line $x+y=5$ excluding points on this line represented by the shaded part.

This can be represented as follows: 

 

Posted by

seema garhwal

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