Identify the vertices of the solution region of the system of linear inequalities. (Order your answers from smallest to largest x, then from smallest to largest y.)

x ≥ −2
x ≤ 3
y ≤ 5
y ≥ x

(x, y) =
(x, y) =
(x, y) =
(x, y) =

Tried several times, just can't get this - Help!

The vertices involving y>=x are clearly

(-2,-2) and (3,3)

The rest you can surely find...

What did you try?

See the solutions at

http://www.wolframalpha.com/input/?i=solve+x+%E2%89%A5+%E2%88%922%2C+x+%E2%89%A4+3%2C+y+%E2%89%A4+5%2C+y+%E2%89%A5+x+

To find the vertices of the solution region, we need to identify the points where the lines formed by the inequalities intersect.

First, let's solve the system of linear inequalities:

We have the following inequalities:
1) x ≥ -2
2) x ≤ 3
3) y ≤ 5
4) y ≥ x

To solve the system, we can graph each inequality and find the overlapping region.

1) Start by graphing the line x = -2. This is a vertical line passing through x = -2 on the x-axis. Shade the area to the right of this line since we want x to be greater than or equal to -2.

2) Next, graph the line x = 3. This is a vertical line passing through x = 3 on the x-axis. Shade the area to the left of this line since we want x to be less than or equal to 3.

3) Then, graph the line y = 5. This is a horizontal line passing through y = 5 on the y-axis. Shade the area below this line since we want y to be less than or equal to 5.

4) Finally, graph the line y = x. This is a line with a slope of 1 passing through the origin (0,0). Shade the area above this line since we want y to be greater than or equal to x.

By inspecting the graph, we can see that the overlapping region forms a quadrilateral.

The vertices of the solution region are the points where lines intersect. In this case, the vertices are as follows:

(x, y) = (-2, -2)
(x, y) = (3, 3)
(x, y) = (3, 5)
(x, y) = (-2, 5)

Therefore, the vertices of the solution region of the system of linear inequalities are:

(-2, -2), (3, 3), (3, 5), (-2, 5)

To identify the vertices of the solution region, we need to find the points where the lines corresponding to the linear inequalities intersect each other.

Let's begin by graphing each inequality on a coordinate plane.

1. The inequality x ≥ -2 represents a vertical line that passes through the point (-2, y). Since x is always greater than or equal to -2, the line will be a solid line.

2. The inequality x ≤ 3 represents a vertical line that passes through the point (3, y). Similarly, since x is always less than or equal to 3, the line will be a solid line.

3. The inequality y ≤ 5 represents a horizontal line that passes through the point (x, 5). It represents all the points below or on the line, so the line will be a solid line.

4. The inequality y ≥ x represents a diagonal line that passes through the points (x, x) for all x-values. The line represents all the points above or on the line, so the line will be a solid line.

Now, let's find the points where these lines intersect:

1. The vertical line x ≥ -2 intersects the horizontal line y ≤ 5 at the point (-2, 5).

2. The vertical line x ≤ 3 intersects the diagonal line y ≥ x at the point (3, 3).

3. The horizontal line y ≤ 5 intersects the diagonal line y ≥ x at the point (5, 5).

So the vertices of the solution region are as follows:

(3, 3)
(3, 5)
(-2, 5)
(5, 5)

Make sure to order the vertices from smallest to largest x, and then from smallest to largest y.