Question

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

Answer 1

`\begin{gathered} B)\:\:y\geqslant(4x)/(5)-(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 \\ \\ (-5y)/(-5)\leq(1)/(-5)+(-4x)/(-5) \\ \\ y\ge(4x)/(5)-(1)/(5) \end{gathered}`

And the second inequality:

`\begin{gathered} (1)/(2)y-x\leq3 \\ \\ (1)/(2)y\leq3+x \\ \\ 2*(1)/(2)y\leq(3+x)*2 \\ \\ y\leq6+2x \end{gathered}`

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

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

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