Question

Solve for x and y

99x + 101y=499xy

101x +99y= 501xy

Answer 1

Consider 99x+101y=499xy_______(1) 101x+99y=501xy ________(2)
multiplying equation (1) by -101 we get
-9999x-10201y=-50,399xy______(3)
multiplying equation (2) by 99
9999x+9801y=49,599xy___________(4)
adding (3) and (4) we get
-400y=-800xy
x=1/2
substituting x=1/2 in equation (1) we get
99×1/2+101y=499×1/2×y
99/2=(499/2-101)y
99=297y
y=99/297
y=1/3
check
99×1/2+101×1/3=499/6