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

Answer is (iii) infinitely many solution

for every value of x , there is a corresponding value of y, so option (iii) infinitely many solutions is the correct option.

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

Using X = 0

y = 3(0) + 5
y = 5
(0, 5) is your solution

Using x = 1

y = 3(1) + 5
y = 8
(1, 8) is your solution

Using x = 2

y = 3(2) + 5
y = 11
(2, 11) is your solution

So whatever x value you use, there is a corresponding y value. There are infinite solutions.