Question

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

Answer 1

In the given two variable, if we put the value of $x$, then we get the corresponding value of $y$

if value of $x=0$ then

$\Rightarrow y=3\times 0+5$

$\Rightarrow y=5$

if value of $x=1$ then

$\Rightarrow y=3\times 1+5$

$\Rightarrow y=8$

if value of $x=2$ then

$\Rightarrow y=3\times 2+5$

$\Rightarrow y=11$

if value of $x=-1$ then

$\Rightarrow y=3\times -1+5$

$\Rightarrow y=2$

Hence, all these pairs $(0,5),(1,8),(2,11),(-1,2)$ are the solution for the given pair of equation

Hence, the given equation had infinitely many solutions.