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

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Solution

y = 3x + 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).

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Similar questions

Q. Question 1
Which one of the following options is true, and why?

y = 3 x + 5

has
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions

Question 1 (ii)
Which of the following pairs of linear equations has a unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
2x + y = 5 ; 3x +2y =8

Q. Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions.
(i)

x - 3 y - 3 = 0; 3 x - 9 y - 2 = 0

(ii)

2 x + y = 5; 3 x + 2 y = 8

(iii)

3 x - 5 y = 20; 6 x - 10 y = 40

(iv)

x - 3 y - 7 = 0; 3 x - 3 y - 15 = 0

Q. Question 1 (iii)
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.
3x - 5y = 20 ; 6x - 10y =40

Q. For which value(s) of

λ

, do the pair of linear equations

λ x + y = λ^{2}

and

x + λ y = 1

have
(i) no solution ? (ii) infinitely many solutions ?

(iii) a unique solution ?

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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

y = 3x + 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).

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

y = 3x + 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).