Math, asked by shashank9922, 1 year ago

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Answers

Answered by Anonymous
14

Question:

Solve:

5/(x-1) + 1/(y-2) = 2 and 6/(x-1) - 3/(y-2) = 1

Answer:

x = 4 , y = 5

Solution:

We have;

5/(x-1) + 1/(y-2) = 2 --------(1)

6/(x-1) - 3/(y-2) = 1 --------(2)

Let ; 1/(x-1) = a and 1/(y-2) = b

Now ,

Putting 1/(x-1) = a and 1/(y-2) = b in the eq-(1) and eq-(2) , we get;

5a + b = 2 -------(3)

6a - 3b = 1 -------(4)

Now ,

Multiplying both sides of eq-(3) , we get;

=> 3•(5a + b) = 3•2

=> 15a + 3b = 6 -------(5)

Now,

Adding eq-(4) and eq-(5) , we get ;

=> 6a - 3b + 15a + 3b = 1 + 6

=> 21a = 7

=> a = 7/21

=> a = 1/3

=> 1/(x-1) = 1/3

=> x - 1 = 3

=> x = 3 + 1

=> x = 4

Now,

Putting a = 1/3 in eq-(4) , we get ;

=> 6a - 3b = 1

=> 6•(1/3) - 3b = 1

=> 6/3 - 3b = 1

=> 2 - 3b = 1

=> 3b = 2 - 1

=> 3b = 1

=> b = 1/3

=> 1/(y-2) = 1/3

=> y - 2 = 3

=> y = 3 + 2

=> y = 5

Hence,

The solution of the given system of equations is;

x = 4

y = 5

Answered by raneankita155
1

Answer:

let x-1 be m and y-2 be n

Step-by-step explanation:

5m+1n=2 , 6m-3n=1

multiply eqn by 3= 15m+3n=6

by subtracting

15m+3n=6

6m-3n=1

ans is 8m=4

m=4/8

=1/2

substitute m=1/2 in eqn 1

=15*1/2+3n=6

=15/2+3n=6

=7.5+3n=6

=3n=6-7.5

=3n=-1.5

n=-1.5/3

n=-0.3

place m=x-1 and n =y-2

m=x-1

=1/2=x-1

=2(x-1)

=2x-2=0

2x=2

X=2/2

X=1

place n=y-2

0.3=y-2

0.3+2=y

2.3=y

ANS =(X,y) =1,2.3

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