Solve the following inequalities graphically in two dimensional plane: $3 y - 5 x < 30$

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Solution

Consider: $3 y - 5 x = 30$
$\begin{matrix} x & 0 & - 6 & 3 y & 10 & 0 & 15 \end{matrix}$
Putting $(0, 0)$ in the given inequation, we have $- 3 \times 0 - 5 \times 0 < 30$
$\Rightarrow 0 < 30$ , which is true.
$∴$ Half plane of $3 y - 5 x < 30$ is towards origin.

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