Question

ay 2Given the system of inequalities:4x - 5y ≤ 1y-x<3

Answer 1

$\begin{gathered} B)\:\:y\geqslant\frac{4x}{5}-\frac{1}{5} \\ \:\:\:\:y\leq6+2x \end{gathered}$

1) Since the starting point is those inequalities in the standard form, we need to perform some algebraic manipulations to get them in the slope-intercept form

2) So, let's rewrite them by adding/subtracting and dividing/multiplying terms to isolate the y-term on the left:

$\begin{gathered} 4x-5y\leq1 \\ \\ 4x-4x-5y\leq1-4x \\ \\ -5y\leq1-4x \\ \\ \frac{-5y}{-5}\leq\frac{1}{-5}+\frac{-4x}{-5} \\ \\ y\ge\frac{4x}{5}-\frac{1}{5} \end{gathered}$

And the second inequality:

$\begin{gathered} \frac{1}{2}y-x\leq3 \\ \\ \frac{1}{2}y\leq3+x \\ \\ 2\times\frac{1}{2}y\leq(3+x)\times2 \\ \\ y\leq6+2x \end{gathered}$

3) Examining the options, we can tell that the answer is:

$\begin{gathered} B)\:I)\:y\geqslant\frac{4x}{5}-\frac{1}{5} \\ \:\:\:II)\:y\leq6+2x \end{gathered}$

Thus, the answer is the second option (top to bottom).