Question

7x-2y/xy=5 ; 8x+7y/xy=15 Solve the simultaneous equation

Answer 1

(7x - 2y)/xy = 5 and (8x + 7y)/xy = 15

(7x - 2y)/xy = 5
=> 7x - 2y = 5xy
dividing xy from both sides,
7x/xy - 2y/xy = 5xy/xy
=> 7/y - 2/x = 5 ------(1)

Similarly, (8x + 7y)/xy = 15
=> 8x/xy + 7y/xy = 15
=> 8/y + 7/x = 15 ------(2)

multiply 2 with equation (2) and 7 with equation (1) and then add.

7(7/y - 2/x) + 2(8/y + 7/y) = 7 × 5 + 2 × 15
=> 49/y -14/x + 16/y + 14/y = 35 + 30
=> 65/y = 65
=> y = 65/65 = 1
put y = 1 in equation (1),
7/1 - 2/x = 5
=> -2/x = 5 - 7 = -2
=> x = 1

hence, x = 1 and y = 1

Answer 2

Given :
(7x - 2y)/xy = 5……….(1)
(8x + 7y)/xy = 15……….(2)

From eq. 1,
(7x - 2y)/xy = 5
7x - 2y = 5xy ………(3)

Divide eq 3 by xy both sides,
7x/xy - 2y/xy = 5xy/xy
7/y - 2/x = 5 …………(4)

From eq. 2,
(8x + 7y)/xy = 15
8x + 7y = 15xy………….(5)

Divide eq 5 by xy both sides,
8x/xy + 7y/xy = 15xy/xy
8/y + 7/x = 15 ………….(6)

Let 1/y = p & 1/x = q
Eq. 4 becomes :
7p - 2q = 5……….(7)
Eq. 6 becomes :
8p + 7q = 15……….(8)

BY SUBSTITUTION METHOD
From eq 7,
7p = 5 +2q
p = (5+2q)/7……….(9)

On Substituting p = (5+2q)/7 in eq 8,
8p + 7q = 15
8(5+2q)/7 + 7q = 15
(40 + 16q)/7 + 7q = 15
(40 + 16q + 49q)/7 = 15
65q +40 = 15 × 7
65q +40= 105
65q = 105 - 40
65 q =65
q = 65/65 = 1
q = 1

On putting q= 1 in eq 8,
p = (5+2q)/7
p = (5+2×1) /7
p = (5+2)/7= 7/7 = 1
p = 1

1/y = p [ p = 1]
1/y = 1
y = 1

1/x = q [q = 1]
1/x = 1
x =1

Hence, the solution of the given system of equation is x = 1 and y = 1

HOPE THIS WILL HELP YOU..