Find the value of‘a’ and ‘b’ for which the following system of linear equations has infinite number of solutions :

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

A railway half-ticket costs half the full-fare but the reservation charges arc the same on a half-ticket as on a full ticket. One reserved first class ticket from station A to station B costs Rs. 2125. Also one reserved first class ticket and one reserved half-first class ticket from A to B cost Rs. 3200. Find the full fare from station A to B and also the reservation charges for a ticket.

Latakshi started her job in the begining of year 1991 with a slary of Rs. x per month and earned an yearly increment of Rs. y, if her salary at the begining of year 1996 was Rs. 3,000 and at the begining of year 2000 was Rs. 4,200; find

(i) the values of x and y. (ii) Latakshi’s monthly salary during 1994 and during 1999.

 Draw the graphs of the following equations on the same graph paper. 2x + 3y = 12, x - y = 1 .

Find the co-ordinates of the vertices of the triangle formed by the two straight lines and the y-axis.

70. Find the values of α and β for which the following system of linear equations has infinite number of solutions 2x + 3y = 7, 2αβ + (α + β)y = 28.