Question

solving a system of linear inequalities given the system of inequalities: $4x - 5y \leq 1$ $\frac{1}{2}y - x \leq 3$ which shows the given inequalities in slope - intercept form? $\circ$ $y \leq \frac{4}{5}x - \frac{1}{5}$ $y \leq 2x + 6$ $\circ$ $y \geq \frac{4}{5}x - \frac{1}{5}$ $y \leq 2x + 6$ $\circ$ $y \geq -\frac{4}{5}x + \frac{1}{5}$ $y \geq 2x + 6$

Explanation:

Step1: Rearrange first inequality

Start with $4x - 5y \leq 1$. Isolate $y$:
$-5y \leq -4x + 1$
Divide by $-5$ (reverse inequality sign):
$y \geq \frac{4}{5}x - \frac{1}{5}$

Step2: Rearrange second inequality

Start with $\frac{1}{2}y - x \leq 3$. Isolate $y$:
$\frac{1}{2}y \leq x + 3$
Multiply by 2:
$y \leq 2x + 6$

Answer:

$y \geq \frac{4}{5}x - \frac{1}{5}$
$y \leq 2x + 6$
(This corresponds to the second multiple-choice option)