Multiple Choice Question A system of linear inequalities is given. 12x+6>2y13y<23x Which graph shows the solution to this system of inequalities? A. B. C. D.

Answer 1

To solve the system of inequalities given by:

1. \( 12x + 6 > 2y \)
2. \( 13y < 23x \)

we can first rewrite each inequality in the slope-intercept form \(y = mx + b\).

1. For \( 12x + 6 > 2y \):

   • Rearranging gives \( 2y < 12x + 6 \), or \( y < 6x + 3 \).

2. For \( 13y < 23x \):

   • Rearranging gives \( y < \frac{23}{13}x \).

Now we have two inequalities:

• \( y < 6x + 3 \)
• \( y < \frac{23}{13}x \)

The solution will be the region below both lines on the graph.

To determine which graph represents this solution, look for a graph that displays the area below the line \( y = 6x + 3 \) and below the line \( y = \frac{23}{13}x \).

You would typically look for:

• The line \( y = 6x + 3 \) has a y-intercept of 3 and a slope of 6.
• The line \( y = \frac{23}{13}x \) has a positive slope of approximately 1.77 (since \( 23/13 \approx 1.77\)) and passes through the origin.

The feasible region is where both shaded areas overlap.

Since you have four options (A, B, C, D) and I cannot see the graphs, you should select the graph that shows the area below both lines. If any of the graphs correctly illustrates the area below both of these constraints, that is your answer.

If you have any more specific details about the graphs, feel free to share!