the solution to each systen \( \left\{y \geq-\frac{5}{3} x+2 y \geq-3\right. \)

To solve the system of inequalities, start by graphing the lines represented by the equations. The first inequality, \(y \geq -\frac{5}{3}x + 2\), has a y-intercept of 2 and a slope of \(-\frac{5}{3}\). The second inequality, \(y \geq -3\), represents a horizontal line at \(y = -3\). The solution to the system consists of the region above both lines and includes the boundaries since the inequalities are non-strict. To find the intersection of these lines, set them equal: \[ -\frac{5}{3}x + 2 = -3. \] Solving for \(x\): \[ -\frac{5}{3}x = -5 \Rightarrow x = 3. \] Plugging \(x = 3\) into one of the inequalities, \(y = -3\). Therefore, the point \((3, -3)\) lies on both boundaries and will be included in the solution region. The solution to the system is all points \((x, y)\) that lie in the shaded region above both lines on a graph.