RBSE Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Additional Questions

RBSE Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Additional Questions is part of RBSE Solutions for Class 9 Maths. Here we have given Rajasthan Board RBSE Class 9 Maths Solutions Chapter 4 Linear Equations in Two Variables Additional Questions.

Board	RBSE
Class	Class 9
Subject	Maths
Chapter	Chapter 4
Chapter Name	Linear Equations in Two Variables
Exercise	Additional Questions
Number of Questions Solved	10
Category	RBSE Solutions

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 4 Linear Equations in Two Variables Additional Questions

Multiple Choice Questions

Question 1.
The lines representing the (RBSESolutions.com) linear equations 2x – y – 3 and 4x – y = 5
(A) intersect at a point
(B) are parallel
(C) are coincident
(D) intersect at exactly two points
Solution.
The given lines are
2x – y = 3

Thus, lines will intersect at a point. Hence, the correct option is (A).

Question 2.
If the pair of linear equations in (RBSESolutions.com) two variables has infinite number of solutions, then the lines represented by these equations are:
(A) intersecting lines
(B) coincident lines
(C) parallel lines
(D) perpendicular lines
Solution.
If two lines i.e. a pair of linear equations, has infinitely many solutions it means lines are overlapping each other i.e. coincident lines.
Hence, the correct option is (B).

Question 3.
The pair of (RBSESolutions.com) linear equation 5x + 4y = 20 and 10x + 8y = 16 have
(A) no solution
(B) many solutions
(C) two solutions
(D) one solution
Solution.


equations is inconsistent i.e. lines are parallel.
Thus, given pair of linear equations has no solution.
Hence, the correct option is (A).

Question 4.
The value of k for which the pair (RBSESolutions.com) of linear equations 4x + 6y – 1 = 0 and 2x + ky – 7 = 0 represent parallel lines is:
(A) k = 3
(B) k = 2
(C) k = 4
(D) k = – 2
Solution.
When lines are parallel, condition for it is

⇒ 2k = 6 ⇒ k = 3
Hence, the correct option is (A).

Question 5.
If kx + 2y = 5 and 3x + y = 1 has (RBSESolutions.com) a unique solution, if
(A) k = 6
(B) k ≠ 6
(C) k = 0
(D) k has any value
Solution.
Condition for unique solution is

Hence, the correct option is (B).

Question 6.
The value of λ for (RBSESolutions.com) which x + 2y + 7 = 0 and 2x + λy + 14 = 0 represent coincident lines is
(A) 3
(B) 4
(C) – 4
(D) – 3
Solution.
The pair of lines represent coincident lines if


Hence, the correct option is (B).

Question 7.
A pair of (RBSESolutions.com) linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is inconsistent if

Solution.
A pair of linear equations is said to be inconsistent if pair of equations has no solution and condition for no solution is

Hence, the correct option is (D).

Question 8.
If the system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28 represent coincident lines (RBSESolutions.com) then required condition is
(A) b = 2a
(B) a = 2b
(C) 2a + b = 0
(D) a + 2b = 0
Solution.
For coincident lines, condition is

Hence, the correct option is (A).

Question 9.
If the system (RBSESolutions.com) of equations 2x + 3y = 7 and (a + b)x + (2a – b)y = 21 has infinitely many solutions, then
(A) a = 1, b = 5
(B) a = 5, b = 1
(C) a = – 1, b = + 5
(D) a = 5, b = – 1
Solution.
Condition for infinitely many solutions is

Solving (i) and (ii), we get a = 5 and b = 1.
Hence, the (RBSESolutions.com) correct option is (B).

Question 10.
The line 2x – 3y – 6 = 0 meets x-axis at
(A) (0, 3)
(B) (3, 0)
(C) (2, 3)
(D) (6, 2)
Solution.
The line 2x – 3y – 6 = 0 meets x-axis,
where y = 0 i.e. ordinate is zero
⇒ 2x – 3 x 0 – 6 = 0 ⇒ 2x = 6 ⇒ x = 3
Thus, point of intersection of the line with the x-axis is (3, 0).
Hence, the (RBSESolutions.com) correct option is (B).

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