Solve the system of two linear inequalities graphically.

Question

{2x+6y<−18 x≥3 Find the region with points that satisfy both inequalities. Select the region you wish to be shaded: A B, C or D

Answer 1

To graphically solve the system of inequalities, we need to graph each inequality separately and then find the overlapping region.

Let's start by graphing the inequality 2x + 6y < -18.

First, we need to find the equation in slope-intercept form (y = mx + b).

2x + 6y < -18
6y < -2x - 18
y < (-2/6)x - 3
y < (-1/3)x - 3

Now, let's graph this inequality:

1. Plot the y-intercept: -3. This gives us the point (0, -3).
2. Find another point using the slope. The slope is -1/3, so from the point (0, -3), move right 3 units and down 1 unit. This gives us the point (3, -4).
3. Draw a dashed line through these two points.

Next, let's graph the inequality x ≥ 3.

1. Plot a vertical line on x = 3. Make the line solid.

Now, let's find the overlapping region. The shaded region will satisfy both inequalities.

The overlapping region is represented by the shaded region C.