Question

Solve for x and y, using elimination method

6/(x+y)= 7/(x-y) + 3

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

Answer 1

let 6/(x+y) = 7/(x-y) +3 .........eq. (1) & 1/2(x+y) = 1/3(x-y) ......eq.(2)

Now from eq.2
we have 1/2(x+y) = 1/3(x-y)
or 3x-3y = 2x+2y
or 3x-2x = 3y+2y
or x = 5y..... .....eq.(3)

Putting value of x in eq. (1)
we have 6/(5y+y) = 7/(5y-y) +3
or 6/6y = 7/4y +3
or 1/y = (7+12y)/4y
or 12y.y + 7y = 4y (by cross multiplication)
or 12y.y. + 3y = 0
or 3y(4y+1) =0
or 4y+1 = 0
or y= -1/4

putting the value of y in eq.(3)

we get x=5(-1/4) = -5/4

so. Ans. x=-5/4, y = -1/4