Question

Find the value of a, so that the point (3, a) lies on the line 2x − 3y = 5.

Answer 1

$$\begin{gathered} \text{The point}\left(3,a\right)\text{lies on the line}2x-3y=5. \\ \mathrm{If}\mathrm{point}\left(3,a\right)\mathrm{lies}\mathrm{on}\mathrm{the}\mathrm{line}2x-3y=5,\mathrm{then} \\ 2x-3y=5 \\ \Rightarrow \left(2\times 3\right)-\left(3\times a\right)=5 \end{gathered}$$
$$\begin{gathered} \Rightarrow 6-3a=5 \\ \Rightarrow 3a=1 \\ \Rightarrow a=\frac{1}{3} \end{gathered}$$
$\text{Hence, the value of}a\text{is}\frac{1}{3}$.