Consider the following two statements
$\mathrm{I}$. Any pair of consistent liner equations in two variables must have a unique solution.
$\mathrm{II}$. There do not exist two consecutive integers, the sum of whose squares is $365$ .

Then

• A

  both $\mathrm{I}$ and $\mathrm{II}$ are true
   
• Correct answer
  B

  both $\mathrm{I}$ and $\mathrm{II}$ are false
   
• C

  $\mathrm{I}$ is true and $\mathrm{II}$ is false
   
• D

  $\mathrm{I}$ is false and $\mathrm{II}$ is true

Hence, the correct answer is option: 'B'.