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 $4x - 5y\leq1$, subtract $4x$ from both sides: $- 5y\leq1 - 4x$. Then divide by $-5$. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $y\geq\frac{4}{5}x-\frac{1}{5}$.

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:

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