Solve the following inequalities graphically in two-dimensional plane:

x – y ≤ 2

Given: x – y 2

Consider: x – y = 2


X



0



2



Y



-2



0



Now draw a solid line x – y = 2 in the graph (∵ x – y = 2 is included in the given question)


Now Consider x – y ≤ 2


Select a point (0,0)


⇒ (0) – (0) ≤ 2


⇒ 0 ≤ 12 (this is true)


∴ Solution region of the given inequality is above the line x – y = 2. (That is origin is included in the region)


The graph is as follows:



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