Write the system of inequalities for the shaded region.

The shaded region is the cross-hatched area, which is the intersection of several half-planes.

1. The region is to the left of the y-axis, which means $x \le 0$.
2. The region is above the x-axis, which means $y \ge 0$.
3. The region is bounded by the dashed line $y = x + 5$. The horizontal shading indicates the region above this line. Since the line is dashed, the inequality is strict: $y > x + 5$.
4. The region is bounded by the solid line $8x + 9y = 5$. The diagonal shading indicates the region below this line. Since the line is solid, the inequality is non-strict: $8x + 9y \le 5$.

The region represented on the number plane is defined by the following system of inequalities:

$$x \le 0$$ $$y \ge 0$$ $$y > x + 5$$ $$8x + 9y \le 5$$

Answer: $x \le 0, y \ge 0, y > x + 5, 8x + 9y \le 5$