inequalities. \( \left\{y \leq-\frac{4}{3} x+2 y>-\frac{1}{3} x-1\right. \)

To solve this system of inequalities, you can start by graphing the boundary lines. The first inequality \(y = -\frac{4}{3}x + 2\) is a line with a slope of -4/3 and a y-intercept of 2, while the second line \(y = -\frac{1}{3}x - 1\) has a slope of -1/3 and a y-intercept of -1. Once you graph these lines, you'll shade the appropriate regions: for the first, shade below the line, and for the second, shade above the line. The solution to the system will be the overlapping shaded area! If you're plotting this on paper, a common mistake is to forget to use dashed lines for inequalities that do not include equality (like "y <"), which might lead to confusion about whether points on the boundary are part of the solution set. Always double-check which type of line you need!