Unit Test: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10 PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers  9 to 11 carry 3 marks each.
• Question number 12 & 13 carry 5 marks each.

Q1: Which of the following options represents a pair of linear equations in two variables?  (1 Mark) 
(a) 2x + 3y = 7
(b) x² + y² = 25
(c) 4x + 2y = 10
(d) 3x + 2y² = 8
Ans: (a)

Q2: The number of solutions for a pair of linear equations in two variables can be:  (1 Mark) 
(a) One
(b) Two
(c) Three
(d) None

Q3: If two lines represented by a pair of linear equations are parallel, then:  (1 Mark) 
(a) They intersect at one point
(b) They do not intersect
(c) They intersect at two points
(d) None of the above

Q4: Solve the pair of equations: 2x - 3y = 7 and 4x - 6y = 14.  (1 Mark) 

Q5: Check the consistency of the pair of linear equations and solve them graphically:  (1 Mark) 
4x - 3y = 9
8x - 6y = 18

Q6: Solve the pair of linear equations:  (2 Marks) 
x - y = 4
2x + 3y = 10

Q7: Find the value of 'k' for which the following system of equations has no solution:  (2 Marks) 
2x + 3y = 5
4x + ky = 10

Q8: A sum of money amounts to Rs. 11,000 after 3 years and Rs. 13,750 after 5 years, when it is invested at a certain rate of simple interest. Calculate the rate of interest using a pair of linear equations in two variables.  (2 Marks) 

Q9: The sum of the digits of a two-digit number is 9. If we add 9 to the number, the digits get reversed. Find the number using a pair of linear equations in two variables.  (3 Marks) 

Q10: Solve the following system of equations using any appropriate method:  (3 Marks) 
3x - 2y = 8
6x - 4y = 16

Q11: Solve the pair of linear equations:  (3 Marks) 
2x + y = 7
x - 3y = -4

Q12: The perimeter of a rectangle is 46 meters. The length is 4 meters more than twice the width. Find the dimensions of the rectangle using a pair of linear equations.  (5 Marks) 

Q13: A two-digit number is 6 times the sum of its digits. If 9 is added to the number, the digits interchange their places. Find the number using a pair of linear equations.  (5 Marks)