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

Find the value of x , y 2x+3y=6 3x-2y=4 .

Solve the following system of equations: 1/(2x)+1/(3y)=2,\ \ \ 1/(3x)+1/(2y)=(13)/6

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

Find the value of x , if [(3x+y,-y),(2y-x,3)]=[(1, 2),(-5, 3)] .

Find the value of k so that the lines (1-x)/(3) = (y-2)/(2k) = (z-3)/(2) and (1+x)/(3k) = (y-1)/(1) = (6-z)/(7) are perpendicular to each other.

Find the values of x and y , if 2[(1, 3),( 0,x)]+[(y,0),( 1, 2)]=[(5, 6),( 1 ,8)] .

Evaluate x and y if [(x,2),(-3,y)]=2[(x^(2),1),(-(3)/(2),3y-5)] .

If x=4 and y=1, find the value of ((x)/(2)-(y)/(3))((x^(2))/(4)+(xy)/(6)+(y^(2))/(9)) .

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

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