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

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Solution

Since the equation, $y = 3 x + 5$ is a linear equation in two variables, it will have infinitely many solutions.
Different values of $x$ gives corresponding values of $y$ .

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Similar questions

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

For which value(s) of λ, do the pair of linear equations λx + y = \lambda ^{2} and x + λy = 1 have

(i) no solution?

(ii) infinitely many solutions?

(iii) a unique solution?

Q. Question 2
The pair of equation x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has
(A) a unique solution
(B) exactly two solutions
(C) infinitely many solutions
(D) no solution

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. 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

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General Form of a Linear Equation in Two Variables

Standard X Mathematics

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Question 1 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

Since the equation, y=3x+5 is a linear equation in two variables, it will have infinitely many solutions. Different values of x gives corresponding values of y.

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

Since the equation, $y = 3 x + 5$ is a linear equation in two variables, it will have infinitely many solutions.
Different values of $x$ gives corresponding values of $y$ .