show graphically that the solution set of the following system of inequalities is empty

x-2y greater than = 0, 2x-y less than = -2 ,x greater than = 0, y greater than = 0

Given, x- 2y ≥ 0, 2x - y ≤ -2, x ≥ 0, y ≥ 0

On converting the given inequations into equations, we get

x- 2y = 0, 2x - y = -2, x = 0, y = 0

Now, consider the line x - 2y = 0. Its solution set is:

x02
y01

We find that (0,0) satisfies the inequation x- 2y ≥ 0.  So, the portion containing the origin represents the solution set of the inequation x- 2y ≥ 0.

Again, consider the line 2x - y = -2. Its solution set is:

x0-1
y20

We find that (0,0) doesn't satisfy the inequation 2x - y ≤ -2.  So, the portion not containing the origin represents the solution set of the inequation 2x - y ≤ -2.

Clearly, x ≥ 0 and y ≥ 0 represents the first quadrant.

As all the four lines doesn't possess any common region. So, the solution set of the given linear inequations is empty.

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