Question

Solve the following systems of equations:
(7x – 2y)/xy = 5
(8x + 7y)/xy = 15

Answer 1

Answer:

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Answer 2

x = 1 ; y = 1

Step-by-step explanation:

(7x – 2y)/xy = 5

7x -2y = 5xy

Dividing by xy, we get:

7/y -2/x = 5

Let 1/x be u and 1/y be v, then equation is -2u + 7v = 5 ----------(1)

(8x +7y=xy)/xy = 15

8x +7y = 15xy

Dividing by xy, we get:

8/y +7/x = 15.

(8x + 7y)/xy = 15

Let 1/x be u and 1/y be v, then equation is 7u + 8v = 15 ----------(2)

(1) * 7 = -14u + 49v = 35

(2) * 2 =  14u + 16v = 30

Adding we get: 65v = 65.

Therefore v = 1

Substituting in equation 1, we get: -2u + 7 = 5.

Therefore u = 1

v = 1, so 1/y = 1. Therefore y = 1

v = 1, so 1/x = 1. Therefore x = 1

Hence solved.