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Solve the following system of inequality graphically.

x + y ≤ 9, y ≥ x, x ≥ 0

First, we draw the graph of line x + y = 9

x 0 9

y 9 0

Now, consider the point O(0, 0), i.e, origin.

Substitute in inequality x + y ≤ 9, i.e., 0 + 0 ≤ 9 or 0 ≤ 9 which is true. Therefore, origin is solution of inequality x + y ≤ 9. Therefore, we mark that region which contains origin.

Now, we draw the line y = x or y - x = 0

x 0 1 2

y 0 1 2

Let us consider the point (1, 0).

Substitute it in inequality y ≥ x, i.e., 0 ≥ 1 which is not true.

∴ We mark that region which does not contain point (1, 0).

For x ≥ 0, we mark the region on right side of the line x = 0.

Now, we shade the common region. Thus, the solution is given by the triangular region OAB as shown in the graph.