Question
Solve 3x + 2y > 6 graphically.
✓
Answer
Graph of 3x + 2y = 6 is given as a dotted line in the figure.
This line divides the XY-plane into two half-planes I and II. We select a point (not on the line), say (0, 0), which lies in one of the half-planes and determine if this point satisfies the given inequality or not. we note that
3 (0) + 2 (0) > 6
$\Rightarrow$ 0 > 6, which is not true.
Hence, half-plane I is not the region of the given inequality. Clearly, any point on the line does not satisfy the given strict inequality. In other words, the shaded half-plane II excluding the points on the line is the solution region of the inequality.
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