Question

Select the correct answer.Graph the following system of inequalities.y ≤ 2x + 1 and y < - x - 1

Answer 1

Graph Z

Given the system of inequalities:

`\begin{gathered} y\leqslant2x+1 \\ y<-x-1 \end{gathered}`

To determine which graph is the correct option, we first determine the x and y-intercepts of both inequalities.

`\begin{gathered} y\leqslant2x+1 \\ \text{When y=0, x=-0.5 }\implies(-0.5,0) \\ \text{When x=0, y= 1}\implies(0,1) \end{gathered}`

To determine which side would be the required region, we do the origin (0,0) test.

`\begin{gathered} In\text{ }y\leqslant2x+1,\text{ at (0,0)} \\ 0\leqslant1 \end{gathered}`

This means the origin (0,0) is in the required region.

The correct graph would be Z.