which graph shows the solution to the system of linear inequalities?\nx + 5y≥5\n y≤2x + 4

Explanation:

Step1: Rewrite the first inequality in slope - intercept form

Rewrite $x + 5y\geq5$ as $y\geq-\frac{1}{5}x + 1$. The boundary line is $y=-\frac{1}{5}x + 1$ and the region above this line (since $y$ is greater than or equal) is part of the solution.

Step2: Analyze the second inequality

The second inequality is $y\leq2x + 4$. The boundary line is $y = 2x+4$ and the region below this line (since $y$ is less than or equal) is part of the solution.

Step3: Find the intersection region

The solution to the system of inequalities is the region that satisfies both inequalities simultaneously, which is the intersection of the regions defined by each inequality.

Answer:

The graph that has the region above the line $y=-\frac{1}{5}x + 1$ and below the line $y = 2x+4$ is the correct one. Without seeing all the options, we can't specifically pick an option from the given image (as it seems incomplete), but the described region - intersection is the solution region for the given system of linear inequalities.