Question

Solve the following system of equations by reducing them to a pair of linear equations:

14/ 2x-1 + 15/ y-2 =7
63/ 2x-1 - 21/y-2 =2

Answer 1

Step-by-step explanation:

Let, 1/2x-1=a

and,1/y-2 = b

Therefore, 14a+15b=7 ____________(i)

63a-21b=2 ________________________(ii)

(i)*9 - (ii)*2

126a+135b-126a+42b=63-4

=> 177b=59

=> b = 1/3

Put the value of b in equation no (i)

14a+ 15*1/3=7

=>14a+5=7

=> 14a =2

=> a = 1/7

Again,

1/2x-1=a

=> 1/2x-1 =1/7

=> 2x-1=7

=>2x=8

=> x = 4

and

1/y-2=b

=>1/y-2=1/3

=> y-2=3

=> y=5

The answer is x=4, y=5