[" (i) "2x+3y=7,(a+b)x+(2a-b)y=3],[" (ii) "(2a-1)x-3y=5,3x+(b-2)y=3]

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 + ( 2a - b ) y = 21 .

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

Factorize each of the following algebraic expressions: (i) x^3(a-2b)+x^2(a-2b) (ii)2x-3y)(a+b)+(3x-2y)(a+b) (iii)4\ (x+y)(3a-b)+6(x+y)(2b-3a)

On comparing the ratios (a_(1))/(a_(2)),(b_(1))/(b_(2)) and (c_(1))/(c_(2)), find out whether the following pair of linear equations are consistent,or inconsistent.(i) 3x+2y=5;2x-3y=7( ii) 2x-3y=8;4x-y=9 (iii) (3)/(2)x+(5)/(3)y=7;9x-10y=14( (iv) 5x-3y=11;-10x+6y=-22( v) (4)/(3)x+2y=8;2x+3y=12

Multiply: (i) ( a/7+(a^2)/9)b y\ (b/2-(b^2)/3) (ii) (3x^2y-5x y^2)b y\ (1/5x^2+1/3y^2)

Simplify : (i) (5x - 9y) - (-7x + y) (ii) (x^(2) -x) -(1)/(2)(x - 3 + 3x^(2)) (iii) [7 - 2x + 5y - (x -y)]-(5x + 3y -7) (iv) ((1)/(3)y^(2) - (4)/(7)y + 5) - ((2)/(7)y - (2)/(3)y^(2) + 2) - ((1)/(7)y - 3 + 2y^(2))

On comparing the ratios (a_1)/(a_2),(b_1)/(b_2) and (c_1)/(c_2) , find out whether the following pair of linear equations are consistent, or inconsistent. (i) 3x+2y=5; 2x-3y = 7 (ii) 2x-3y=8 ; 4x-y=9 (iii) 3/2x+5/3y=7 ; 9x-10y=14 (iv) 5x-3y=11 ; -10x+6y = -22 (v) 4/3 x +2y=8 ; 2x+3y = 12

Expand : (i) (2x+3y)^(3) " " (ii) (5y-3x)^(3) " " (iii) (2a+3b)^(3) .

Expand : (i) (2x+3y)^(3) " " (ii) (5y-3x)^(3) " " (iii) (2a+3b)^(3) .