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

Given, linear equation y = 3x + 5

We know that,

y = 3x + 5 is a linear equation in two variables in the form of ax + by + c = 0

Substituting x = 0, in y = 3x + 5, we get :

⇒ y = 3(0) + 5 = 0 + 5 = 5.

∴ (0, 5) is one solution.

Substituting x = 1, in y = 3x + 5, we get :

⇒ y = 3(1) + 5 = 3 + 5 = 8.

∴ (1, 8) is another solution.

Substituting x = 2, in y = 3x + 5, we get :

⇒ y = 3(2) + 5 = 6 + 5 = 11.

∴ (2, 11) is another solution.

Clearly, for different values of x, we get different values of y.

Thus, y = 3x + 5 has infinitely many solutions.

Hence, Option (iii) is the correct answer.