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Answers
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
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