Find the value of k for which each of the following systems of linear equations has an infinite number of solutions:

kx + 3y = (2k + 1),

2(k + 1)x + 9y = (7k + 1).

Examine which of the following pair of values of x and y is a solution of equation 4x — 3y + 24 = 0.

(i) x = 0, y = 8 (ii) x = — 6, y = 0

(iii) x = 1, y = — 2 (iv) x = – 3,y = 4

(v) x = 1, y = — 2 (vi) x = — 4, y = 2

Examine which of the following points lie on the graph of the linear equation 5x — 3y + 30 = 0.

(i) A (— 6, 0) (ii) B (0, 10)

(iii) C (3, — 5) (iv) D (4, 2)

(v) E (— 9, 5) (vi) F (— 3, 5)

(vii) G (— 9, — 5)

Two water taps together can fill a tank in hours. The tap with longer diameter takes 2 hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

Or

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.

A father’s age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages. Find the present age of the father.

Or

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

Find the value of k for which each of the following systems of equations has no solution:

kx + 3y = k - 3,12x + ky = k.

Find the value of k for which each of the following systems of equations has no solution:

kx + 3y = 3,12x + ky = 6.

Find the value of a for which the following system of equations has unique solution:

4x + py + 8 = 0, 2x + 2y + 2 = 0

A man purchased 47 stamps of 20 p and 25 p for Z 10. Find the number of each type of stamps.