given the system of inequalities: 4x - 5y ≤ 1, 1/2y - x ≤ 3. which shows the given inequalities in slope…

Explanation:

Step1: Rearrange the first - inequality

Starting with (4x - 5y\leq1), we want to solve for (y). First, subtract (4x) from both sides: (-5y\leq1 - 4x). Then divide both sides by (- 5). Remember that when dividing an inequality by a negative number, the direction of the inequality sign changes. So (y\geq\frac{4x - 1}{5}=\frac{4}{5}x-\frac{1}{5}).

Step2: Rearrange the second - inequality

Starting with (\frac{1}{2}y-x\leq3), add (x) to both sides: (\frac{1}{2}y\leq x + 3). Then multiply both sides by (2) to get (y\leq2x + 6).

Answer:

(y\geq\frac{4}{5}x-\frac{1}{5}), (y\leq2x + 6) (the second option in the multiple - choice list)