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Solution of Linear Equation in 2 Variables

Which one of ...

Question

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

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. 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. 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

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

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

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

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

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Solution of Linear Equation in 2 Variables

Standard IX Mathematics

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