Solve the following systems of inequalities graphically 2x + y ≥ 6, 3x + 4y ≤ 12.

3x + 4y ≤ 12 ….(ii)

Graph of inequality (i): Let us draw the graph of the line

2x + y = 6

at y = 0, x = 3, we get the point (3, 0) on x - axis
at x = 0, y = 6, we get the point (0, 6) on y - axis

Putting x = y = 0 in (i) we have 0 > 6 which is false.

Hence, half-plane region not containing the origin is the solution region of the given inequality.

Graph of inequality (ii) : Let us draw the graph of the line 3x + Ay = 12. At y = 0, x - 4 we get the point (4, 0) on x-axis.

At x - 0, y = 3 we get the point (0, 3) on v-axis.

Putting X = y - 0 in (ii) we have 0 ≤ 12 which is true.

Hence, half-plane containing the origin is the solution region of the given inequality.

The common region of the above two regions represents the solution set of the given linear system