`1/(3x+y) + 1/(3x-y) = 3/4`
`1/(2(3x+y)) - 1/(2(3x-y)) = -1/8`

1/(3x+y)+1/(3x-y)=3/4 and 1/(3x+y)-1/(3x-y)= -1/4

6/(x+y)=7/(x-y)+3 , 1/(2(x+y))=1/(3(x-y))

{:(x - y = - 1),(3x + 2y = 12):}

Evaluate : (iv) (3x - (1)/(2y) ) (3x + (1)/( 2y))

{:(x = 2 y - 1),(y = 5 - 3x):}

Find (x+y)-:(x-y), if (i) x=2/3, y=3/2 (ii) x=2/5, y=1/2 (iii) x=5/4, y=(-1)/3

Solve : 8 ^(x+1) = 16 ^(y+2) and ( (1)/(2)) ^(3+x) = ((1)/(4))^(3y)

Find the value of x and y (1)/(2x)+(1)/(3y)=2 (1)/(3x)+(1)/(2y)=(13)/(6)

Let R(x_1, y_1)a n dS(x_2,y_2) be the end points of latus rectum of parabola y^2=4xdot The equation of ellipse with latus rectum R S and eccentricity 1/2 are (a > b) ((3x+1)^2)/(64)+(3y^2)/8=1 ((3x-7)^2)/(64)+(3y^2)/8=1 ((3x+1)^2)/8+(3y^2)/(64)=1 ((3x-7)^2)/8+(3y^2)/(64)=1

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)