CSCE TUTORIAL
Chapter 3 Assignment-1
Pair of Linear Equations in two variables
Class – X Mathematics
Q-1. The pair of linear equations 3x + 5y = 3 and 6x + ky = 8 do not have a solution if k=
a) = 5 b) = 10 c) ≠10 d) ≠ 5
Q-2. The solution of the equation x + y = 5 and x − y = 5 is
a) (0,5) b) (5,5) c) (5,0) d) (10 ,5)
Q-3. The pair of linear equations x = 0 , x = −5 has
a) One solution b) two solution c) infinite no. of solution d) no solution
Q-4. For what value of ‘k’ do the equations 3x – y + 8 = 0 and 6x – ky + 16 = 0 represent coincident lines
a) 1/2 b) −1/2 c) 2 d) -2
Q-5. For what value of ‘k’ for which the system of equations 4x + ky + 8 = 0 and 2x + 2y + 2 = 0 has a unique solution?
Q-6. In how many points do the lines represented by the equations x − y = 0 and x + y = 0 intersect?
Q-7. Find the value of (x + y) if 3x − 2y = 5 and 3y − 2x = 3.
Q-8. Sum of two numbers is 35 and their difference is 13, find the numbers.
Q-9. Find the value of ‘p’ for which the pair of linear equations 2px + 3y = 7 and 2x + y = 6 has exactly one solution.
Q-10. Do the equations y = x and y = x + 3 represent parallel lines?
Case study
- The alumni meet of two batches of a college- batch A & batch B were held on the same day in the same hotel in two separate halls “Rose” and “Jasmine”. The rents were the same for both the halls. The expense for each hall is equal to the fixed rent of each hall and proportional to the number of persons attending each meet. 50 persons attended the meet in “Rose” hall, and the organisers had to pay ₹ 10000 towards the hotel charges. 25 guests attended the meet in “Jasmine” hall and the organizers had to pay ₹ 7500 towards the hotel charges. Denote the fixed rent by ₹ x and proportional expense per person by ₹ y.
- Represent algebraically the situation in hall “Rose”.
- Represent algebraically the situation in hall “Jasmine”.
- What is the fixed rent of the halls?
- Find the amount the hotel charged per person.
Q-2. Draw the graphs of 2x − 3y + 6 = 0 and 2x + 3y − 18 = 0. Find the ratio of areas of triangles formed by the given lines with X-axis and Y-axis.
Q-3. Determine graphically the vertices of the triangle, the equations of whose sides are given below 2y − x = 8; 5y − x = 14; y − 2x = 1
