`2x + 3y =7`,
` (a + b ) x + ( 2a - b ) y = 21`.

Find the value of a and b for which the following system of equations has infinite number of solutions. 2x + 3y = 7, (a + b) x + (2a - b) y = 3 (a + b + 1 ) .

2x + 3y = 7 , (a+b + 1 )x + (a + 2b + 2) y = 4 (a + b ) + 1

Find the values of a and b for which the following pair of equations have infinitely many solutions: (i) 2x + 3y = 7 and 2ax + ay =28-by (ii) 2x + 3y =7, (a-b) x + (a +b) y= 3a + b-2 (iii) 2x - (2a + 5) y =5, (2b +1) x - 9y =15

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

If a, b are noncollinear vectors and A = (x + 4y) a + (2x + y + 1)b, B = (y - 2x +2) a + (2x - 3y - 1) b and 3A = 2B, then (x, y) =

For what values of a and b does the following pair of linear equations have infinitely many solutions ? 2x + 3y = 7 a (x + y) - b (x - y) = 3a + b - 2

If [2x+y,4x,5x-7 4x]=[7 7y-13 y x+6] , then the value of x+y is x=3 , y=1 (b) x=2 , y=3 (c) x=2 , y=4 (d) x=3 , y=3

Factorize each of the following expressions: x a^2+x b^2-y a^2-y b^2 (2) x^2+x y a+x z+y z (3) 2a x+b x+2a y+b y (4) a b-b y-a y+y^2

Find x,y, a and b if [(2x+3y , a+b, 8),(1, 4x + y , 3a-4b)] = [(7,1,8),(1,9,10)] .