which graph shows the solution to the system of linear inequalities?\ny ≥ 2x + 1\ny ≤ 2x - 2

Explanation:

Step1: Analyze slope and y - intercept of first inequality

The inequality $y\geq2x + 1$ has a slope of $m = 2$ and a y - intercept of $b=1$. The line $y = 2x+1$ is solid (because of $\geq$) and the region above the line is shaded.

Step2: Analyze slope and y - intercept of second inequality

The inequality $y\leq2x - 2$ has a slope of $m = 2$ and a y - intercept of $b=-2$. The line $y = 2x - 2$ is solid (because of $\leq$) and the region below the line is shaded.

Step3: Determine the solution region

Since the two lines $y=2x + 1$ and $y=2x - 2$ are parallel (same slope), there is no overlapping shaded region for the system $y\geq2x + 1$ and $y\leq2x - 2$. The solution set of the system is the empty - set.

Answer:

There is no solution (empty - set) as the two parallel lines with the given inequalities do not have an overlapping shaded region.