Question

Solve for x and y:

$\frac{9}{x}-\frac{4}{y}=8,\frac{13}{x}+\frac{7}{y}=101(x\ne 0,y\ne 0).$

Answer 1

⇒ (9/x) - (4/y) = 8 and (13/x) + (7/y) = 101

Elimination method :
⇒ (9/x) - (4/y) = 8 ------(1)
(13/x) + (7/y) = 101----(2)
Multiply equ (1) by 7 and equ (2) by 4

⇒ (63/x) - (28/y) =56 ----(3)
(52/x) + (28/y) = 404 ----(4)

Adding equ(3) and equ (4)

115/x = 460
X =1/4
Substitute x value in equ (4)
208 + (28/y) = 404
28 / y = 196
Y = 1 / 7.