Which one of the following options is true, and why? <br/><br/>$y=3 x+5$ has<br/><br/>(i) a unique solution, <br/><br/>(ii) only two solutions,<br/><br/> (iii) infinitely many solutions

Solution:

$y=3 x+5$ is a linear equation in two variables and it has infinite possible solutions. As for every value of $x$, there will be a value of $y$ satisfying the above equation and vice-versa.

Hence, the correct answer is (iii).