# Solve the Following Systems of Equations: (7x - 2y)/"Xy" = 5 (8x + 7y)/"Xy" = 15 - Mathematics

Solve the following systems of equations:

(7x - 2y)/"xy" = 5

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

#### Solution

(7x - 2y)/"xy" = 5

=> 7/y - 2/x = 5 .....(1)

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

=> 8/y + 7/x = 15 ..........(2)

Let 1/x = p and 1/y = q

The given equations reduce to:

-2p + 7q = 5

=> -2p + 7q - 5 = 0 ...(3)

7p + 8q = 15

=> 7p + 8q - 15 = 0 ....(4)

Using cross multiplication method, we obtain:

p/(-105-(-40)) = q/(-35-30) = 1/(-16-49)

p/(-65) = 1/(-65), q/(-65) = 1/(-65)

p = 1, q= 1

p = 1/x = 1, q= 1/y =1

x = 1 , y = 1

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.3 | Q 42 | Page 46