`(x)/(2)+(2y)/(3)=-1` And `x-(y)/(3)`

(x) / (2) + (y) / (3) = 1 (x) / (3) + (y) / (2) = 1

Solve the following pair of linear equations by the elimination method and the substitution method: (i) x+y=5" "a n d" "2x 3y=4 (ii) 2x+4y=10" "a n d" "2x 2y=2 (iii) 3x 5y 4=0" "a n d" "9x=2y+7 (iv) x/2+(2y)/3=-1 and x-y/3=3

(3) 3x-2y=(5)/(2) (1)/(3)x+3y=-(4)/(3)

Find the following products and verify the result for x=-1,y=-2:(3x-5y)(x+y)(2)(x^(2)y-1)(3-2x^(2)y)((1)/(3)x-(y^(2))/(5))((1)/(3)x+(y^(2))/(5))

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))

If A (x_(1), y_(1)), B (x_(2), y_(2)) and C (x_(3), y_(3)) are vertices of an equilateral triangle whose each side is equal to a, then prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)| is equal to