Chapter I : Linear Equations in two variables in two variables

Exercise - 1

1. For what value of k will the following system of linear equations have no solution?

3x + y = 1, (2k - 1)x + (k - 1)y = 2k +1

2. Determine the value of c for which the following system of linear equations has no solution:

cx + 3y = 3; 12x + cy = 6

3. For what value of k will the system of equations

x + 2y = 5; 3x + ky + 15 = 0

has (i) unique solution (ii) no solution.

4. For what value of k, the following system of equations have (i) a unique solution, (ii) no solutions:

kx + 2y = 5; 3x - 4y = 10

5. Find the value of a and b for which the following system of linear equations has infinite numbers of solutions:

2x - 3y = 7
(a + b)x - (a + b - 3)y = 4a + b.)

Solve the following system of linear equations

6. For the value of k, for which the following system of linear equations has in finite number of solutions:

2x + 3y = 7
(k - 1) x + (k +2)y = 3k

solve the following system of linear equations:

7. 3x - 5y = -1, x - y = -1

8. x + y = 7, 5x + 12y = 7

9. 3x - 4y = 1, 4x - 3y = 6

10. x + y/2 = 4, x/3 + 2y = 5

11. x/3 + y/4 = 4, 5x/6 - y/8 = 4

12. 2/x + 2/3y = 1/6, 3/x + 2/y = 0

13. 2u + 15v = 17uv, 5u + 5v = 36uv

14. 3(a + 3b) = 11ab, 3(2a +b) = 7ab

15. 2x/a + y/b = 2, x/a - y/b = 4

16. x/a - y/b = 0, ax + by = a² + b²

17. (a - b)x + (a +b)y = a² - 2ab - b², (a +b) (x + y) = a² + b²

18. x/a + y/b = a +b, x/a² + y/b² = 2

19. ax + by = c, bx + ay = 1 + c

20. x + y = a - b, ax - by = a² + b²

Answers
(1) 2	(2) 6	(3) (i) (ii)
(4) (i) (ii)		(5) a = -5, b = -1	(6) 7	(7) -2, -1
(8) 11, -4 (13) 5, 1/7	(9) 3, 2 (14) 1, 3/2	(10) 3, 2 (15) 2a, -2b	(11) 6, 8 (16) a, b	(12) 6, -4 (17) a +b, -2ab/(a + b)
(18) a2, b2	(19) (bc - ac + b)/(b2 - a2), (bc - ac - a)/(b2 - a2 )