# Solve Each of the Following Systems of Equations by the Method of Cross-multiplication (X + Y)/(Xy) = 2 (X - Y)/(Xy) = 6 - Mathematics

Solve each of the following systems of equations by the method of cross-multiplication

(x + y)/(xy) = 2

(x - y)/(xy) = 6

#### Solution

The given system of equations is

(x + y)/(xy) = 2

=> x/(xy) + y/(xy) = 2

=> 1/y + 1/x = 2

=> 1/x + 1/y = 2 ............(i)

And

(x - y)/(xy) = 6

=> x/(xy) - y/(xy) = 6

=> 1/y - 1/x = 6

=> 1/x - 1/y = 6   ......(ii)

Taking u = 1/x and v = 1/y we get

u + v = 2 => u + v - 2 = 0 ....(iii)

And u - v = -6 => u - v+ 6 = 0 ........(iv)

Here

a_1 = 1, b_1 = 1,c_1 = -2

a_2 = 1, b_2 = -1, c_2 = 6

By cross multiplication

=> u/(1xx6-(-2)xx(-1)) = v/(1xx6-(-2)xx1) = 1/(1xx(-1) -1 xx1)

=> u/(6-2) = (-v)/(6+2) = 1/(-1-1)

=> u/4 = (-v)/8 = 1/(-2)

Now, u/4 = 1/(-2)

=> u = 4/(-2) = -2

And (-v)/8 = 1/(-2)

=> -v  = 8/(-2) = -4

=> -v = -4

=> v = 4

Now x = 1/u = (-1)/2, y = 1/v = 1/4

Hence x = (-1)/2, y = 1/4 is the solution of the given system of equations.

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.4 | Q 5 | Page 57