Solve the following systems of inequalities, graphically x + y ≤ 9, y > x, x ≥ 0

y > x ...(ii)

x ≤ 0 ...(iii)

Graph of inequality (ii). Let us draw the graph of the line

x + y = 9 ...(iv)

At y = 0, x = 9 we get the point (9, 0) on x-axis.

At x - 0, y = 9 we get the point (0,9) on y-axis.

Putting x = y = 0 in (i) we get 0 ≤ 9 which is true.

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

Graph of inequality (ii). Let us draw the graph of the line y = x
or y - x = 0 ...(v)

on the line (v)

At x = 0⇒ y-0=0 y = 0

At x=1 ⇒ y - 1 =0⇒ y=l

∴ (0, 0) and (1, 1) are on the line (v).

Draw a dotted line joining points (0,0) and(1, 1). To determine the region represented by the given inequality (ii) consider the point not lying on the line (v) say (2, 0) and it lies in the half plane of (ii) if 0 > 2, which is not true. Therefore the portion not containing (2, 0) represents the solution set of the given inequality.

Graph of inequality (iii).

Clearly, x ≥ 0 represents the region lying on the right side of y - axis.

Triple shaded region is the solution region.