Solve the following systems of inequalities graphically x + y>4, 2x - y > 0.

2x - y < 0 ...(ii)

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

x + y = 4 ...(iii)

At y = 0, x = 4 we get the point (4, 0) on x-axis

At x = 0, y = 4 we get the point (0, 4) on y-axis

Putting x = y - 0 in (i) we get 0 > 4 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

2x - y = 0 ...(iv)

On the line (iv)

at x = 0 ⇒ 2(0) -y = 0 ⇒ y = 0

at x = 1 ⇒ 2(1) -y = 0 ⇒ y = 2

(0, 0) and (1, 2) are on the line (iv).

Draw a dotted line joining points (0,0) and (1,2)

To determine the region represented by the given inequality (ii), consider the point not lying on the line (iv), say (2, 1) and it lies in the half-plane of (ii) if 2(2) - 1 < 0, which is not true.

The half-plane region not containing (2, 1) represents the solution set of the given inequality.

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