How do I determine the "best" parametric equation for lines?

Question

Let's say I have to determine the vector equation and the parametric equation for: $$ 2x_1+3x_2=5 $$

How do I determine it the "best" way? I.e. avoiding fractions etc.? Because the answer is: $$ x_1=1+3t, x_2=1-2t $$ How do find that it's a "good idea" to put one of the parameters to 1-2t so the other one becomes nice and neat?

Answer 1

We have $2(x_1-1)=3(1-x_2)$

$\iff\dfrac{x_1-1}3=\dfrac{1-x_2}2=t$(say)