which inequality pairs with y≤ - 2x - 1 to complete the system of linear inequalities represented by the…

Explanation:

Step1: Identify the slope - intercept form

The general form of a linear inequality is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. The given inequality is $y\leq - 2x-1$.

Step2: Analyze the boundary line of the other part of the system

The boundary line of the other part of the system has a positive slope. The y - intercept of the boundary line of the other part of the system is around $y = - 2$. The slope of the line is positive. The equation of a line in slope - intercept form is $y=mx + b$. For the lines in the options, we check the slope and y - intercept. The line we are looking for has a positive slope. Among the options, the lines with positive slopes are of the form $y>2x - 2$ and $y<2x - 2$.

Step3: Determine the correct inequality based on the shading

We can see from the graph that the region above the line $y = 2x-2$ is shaded. So the inequality is $y>2x - 2$.

Answer:

$y>2x - 2$