Unit Test: Pair of Linear Equations in Two Variables

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: Vijay invested certain amounts of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received ₹1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹ 20 more as annual interest. How much money did he invest in each scheme?  (5 Marks) 

Q13: Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?      (5 Marks)

You can find the solutions of this Unit Test here: Unit Test (Solutions): Pair of Linear Equations in Two Variables​