Responding back as requested:

This is all I was provided
Solve the folowing system of linear inequalities by graphing.

x + 2y is less than or equal to 3
2x - 3y is less than or equal to 6

I would change the inequality into slope intercept form and treat it like an equation.

y = mx + b

The first inequality would be:

y < -x/2 + 3/2

I'll leave the rest to you.

I hope this helps. If not, repost with further questions. Thanks for asking.

To solve the given system of linear inequalities by graphing, you can follow these steps:

Step 1: Rewrite the inequalities in slope-intercept form (y = mx + b).

The first inequality, x + 2y ≤ 3, can be rewritten as follows:
2y ≤ -x + 3
y ≤ (-1/2)x + 3/2

The second inequality, 2x - 3y ≤ 6, can be rewritten as follows:
-3y ≤ -2x + 6
y ≥ (2/3)x - 2

Step 2: Graph each inequality on the coordinate plane.

To graph the inequality y ≤ (-1/2)x + 3/2, start by plotting the y-intercept, which is 3/2. Then, use the slope -1/2 to find additional points and draw a line through them. Note that the points on the line should be included in the solution, so make the line solid.

To graph the inequality y ≥ (2/3)x - 2, start by plotting the y-intercept, which is -2. Then, use the slope 2/3 to find additional points and draw a line through them. Note that the points on the line should be included in the solution, so make the line solid.

Step 3: Determine the solution region.

Since you are looking for the intersection of the solution regions, shade the region that satisfies both inequalities. This region will represent the values for x and y that satisfy both conditions simultaneously.

In this case, the shaded region is the area where the shaded region of the first inequality intersects with the shaded region of the second inequality.

Step 4: Identify the solution set.

The solution set consists of all points within the shaded region. You can represent the solution set by shading or listing the points.

I hope this explanation helps you solve the given system of linear inequalities by graphing. If you have any further questions, please let me know.