[" (v) "(a-I)x+3y=2,6x+(1-2b)y=6],[" (vi) "2x+3y=7,(a+b+1)x+(a+2b+2)y=4(a+b)+1]

(a - 1) x + 3y = 2 , 6x + (1 - 2b) y =6 .

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)

Subtract: (i) 5a + 7b - 2c from 3a - 7b + 4c (ii) a - 2b - 3c from -2a + 5b - 4c (iii) 5x^(2) - 3xy + y^(2) from 7x^(2) - 2xy - 4y^(2) (iv) 6x^(3) - 7x^(2) + 5x - 3 from 4 - 5x + 6x^(2) - 8x^(3) (v) x^(3) + 2x^(2) y + 6xy^(2) - y^(3) from y^(3) - 3xy^(2) - 4x^(2) (vi) -11 x^(2) y^(2) + 7xy - 6 from 9x^(2) y^(2) - 6xy + 9 (vii) -2a + b + 6d from 5a - 2b - 3c

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

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

|(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|=|(a_1,b_1,1),(a_2,b_2,1),(a_3,b_3,1)| then the two triangles with vertices (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) and (a_(1), b_(1)), (a_(2), b_(2)), (a_(3), b_(3)) are