Answer
To determine the solution for the given system of inequalities, we start by isolating the y variables. For the first inequality, we add 0.5x to both sides, while for the second inequality, we subtract 1.5x. This gives us: [tex] y geq0.5x+3\yleq -1.5x-1 [/tex] The first inequality has a positive slope, indicating that its line trends upwards, while the second inequality trends downwards. Because y ≥ in the first inequality, the shaded area will be above its corresponding line, which shades regions A and B. Conversely, since y ≤ in the second inequality, the shaded area will be below this line, shading regions A and C. The overlap, which is region A, represents the solution to the system.
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