Which graph represents this system of inequalities? y <_ 2x + 3

3x + y >_ -2

<_ on the second one

y </= 2x+3

y </= -3x - 2 ????

graph it, when do they hit?
(-1, 1)
from there the first one goes up with slope 2
and the second one goes down with slope -3
look at the region BELOW those two lines including the lines

To graph the system of inequalities y ≤ 2x + 3 and 3x + y ≥ -2, follow these steps:

Step 1: Graph y = 2x + 3
- Start by graphing the equation y = 2x + 3, which is a line.
- Since the inequality is y ≤ 2x + 3, the line should be solid (including the points on the line itself).
- Plot two points on the line using any values for x and find their corresponding y-values.
- Draw a straight line through the two points.

Step 2: Shade the area below the line y = 2x + 3
- Since it is y ≤ 2x + 3, shade the area below the line.
- This includes all the points that are below the line, including the points on the line itself.

Step 3: Graph 3x + y ≥ -2
- Graph the equation 3x + y = -2.
- Since the inequality is 3x + y ≥ -2, the line should be solid (including the points on the line itself).
- Plot two points on the line using any values for x and find their corresponding y-values.
- Draw a straight line through the two points.

Step 4: Shade the area above the line 3x + y = -2
- Since it is 3x + y ≥ -2, shade the area above the line.
- This includes all the points that are above the line, including the points on the line itself.

Step 5: Determine the overlapping shaded region
- Look for the overlapping shaded region between the two inequalities.
- This region represents the solution to the system of inequalities.

The correct graph for this system of inequalities would be the shaded region where the two shaded areas overlap.

To find the graph that represents this system of inequalities, we need to graph each inequality separately and then determine the region that satisfies both inequalities.

Let's start with the first inequality: y <= 2x + 3. To graph this, we'll begin by plotting the line y = 2x + 3.

Step 1: Plot two points on the line:
To find the points, you can choose any x values and substitute them into the equation to find the corresponding y values. Let's choose x = 0 and x = 2.

When x = 0, y = 2(0) + 3 = 3. So the first point is (0, 3).
When x = 2, y = 2(2) + 3 = 7. So the second point is (2, 7).

Step 2: Connect the points:
Draw a line passing through the two plotted points. This line represents y = 2x + 3.

Next, let's work on the second inequality: 3x + y >= -2. We'll begin by graphing the line 3x + y = -2.

Step 3: Plot two points on the line:
Let's choose x = 0 and x = -2 to find the corresponding y values.

When x = 0, 3(0) + y = -2, solving for y gives y = -2. So, the first point is (0, -2).
When x = -2, 3(-2) + y = -2, solving for y gives y = 4. So, the second point is (-2, 4).

Step 4: Connect the points:
Draw a line passing through the two plotted points. This line represents 3x + y = -2.

Now that we have the two lines graphed, we need to determine the region that satisfies both inequalities.

Step 5: Shade the region that satisfies both inequalities:
In our case, the solution is where y is less than or equal to 2x + 3 (y <= 2x + 3), and where 3x + y is greater than or equal to -2 (3x + y >= -2). The overlapping region shaded in the graph represents the solution to the system of inequalities.

So, the graph that represents this system of inequalities would be the region where the shaded area formed by the overlapping lines.