1. For what value of k, do the equations 3x – y + 8 = 0 and 6x – ky = – 16

2. A railway half ticket cost half the full fare but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from the stations A to B costs ₹ 2530. Also, one reserved first class ticket and one reserved first class half ticket from stations A to B costs ₹ 3810. Find the full first class fare from stations A to B and also the reservation charges for a ticket.

3. Aruna has only ₹ 1 and ₹ 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹ 75, then the number of ₹ 1 and ₹ 2 coins are, respectively

4. A two-digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

5. The pair of equations x = a and y = b graphically represents lines which are

6. If the lines given by 3x+ 2ky = 2 and 2x + 5y = 1 are parallel, then the value of k is

7. For all real values of c, the pair of equations x – 2y = 8 and 5x – lOy = c have a unique solution. Justify whether it is true or false.

8. Write a pair of linear equations which has the unique solution x = – 1 and y = 3. How many such pairs can you write?

9. Vijay had some bananas and he divided them into two lots A and B. He sold the first lot at the rate of ₹ 2 for 3 bananas and the second lot at the rate of ₹ 1 per banana and got a total of ₹ 400 If he had sold the first lot at the rate of ₹ 1 per banana and the second lot at the rate of ₹ 4 for 5 bananas, his total collection would have been ₹ 460. Find the total nmber of bananas he had.

10. If x = a and y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are, respectively

11. One equation of a pair of dependent linear equations is – 5x+ 7y – 2 = 0. The second equation can be

12. The value of c for which the pair of equations cx- y = 2 and 6x – 2y = 3 will have infinitely many solutions is

13. For the pair of equations λx + 3y + 7 = 0 and 2x + 6y -14 = 0. To have infinitely many solutions, the value of λ should be 1. Is the statement true?

14. The pair of equations y = 0 and y = – 7 has

15. A pair of linear equations which has a unique solution x – 2 and y = – 3 is

16. The line represented by x = 7 is parallel to the X-axis, justify whether the statement is true or not.

17. The pair of equations x + 2y + 5 = 0 and – 3x – 6y +1 = 0 has

18. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in year) of the son and the father are, respectively

19. Graphically, the pair of equations

6x – 3y + 10 = 0

2x – y + 9 = 0

represents two lines which are

20. If a pair of linear equations is consistent, then the lines will be