#### Question

Solve the given inequality graphically in two-dimensional plane: 2*x* + *y* ≥ 6

#### Solution

The graphical representation of 2*x* + *y* = 6 is given in the figure below.

This line divides the *xy*-plane in two half planes, **I** and **II**.

Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not.

We select the point as (0, 0).

It is observed that,

2(0) + 0 ≥ 6 or 0 ≥ 6, which is false

Therefore, half plane **I** is not the solution region of the given inequality. Also, it is evident that any point on the line satisfies the given inequality.

Thus, the solution region of the given inequality is the shaded half plane **II** including the points on the line.

This can be represented as follows.

Is there an error in this question or solution?

Solution Solve the Given Inequality Graphically in Two-dimensional Plane: 2x + Y ≥ 6 Concept: Graphical Solution of Linear Inequalities in Two Variables.