Solve the following inequalities graphically in two-dimensional plane:

2x – 3y > 6

Given: 2x – 3y > 6

Consider: 2x – 3y = 6


X



0



3



Y



-2



0



Now draw a dotted line 2x – 3y = 6 in the graph (∵2x – 3y = 6 is excluded in the given question)


Now Consider 2x – 3y > 6


Select a point (0,0)


⇒ 2 × (0) – 3 × (0) > 6


⇒ 0>5 (this is false)


∴ Solution region of the given inequality is below the line 2x – 3y > 6. (Away from the origin)


The graph is as follows:



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