Question

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

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.
Substitution method :
⇒ (9/x) - (4/y) = 8 ------→(1)
(13/x) + (7/y) = 101------→(2)
From equ (1)
We get 1/x = 1/9(8+4/y)
Subsitute 1/x in equ (2)
13{ 1/9 (8+4/y) } + 7/y = 101
104/9 + 52/9y +7/y = 101 (multiply 9 on both sides)
104 + 52/y +63/y = 909
115/ y = 909-104
115 / y = 805
y = 115 / 805
y = 1/7
Subsitute y in equ (2)
(13/x) + (7/y) = 101
13 /x + 49 = 101
13 / x =52
x = 1 / 4.