Verified answer

Step-by-step explanation:

♦ Given ♦ :-

• 5/x-1 + 1/y-2 = 2.
• 6/x-1 - 3/y-2 = 1

♦ To find ♦ :-

• Solution of the pair of linear equations

♦ Solution ♦ :-

Given pair of linear equations in two variables are:

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

and

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

Put 1/(x-1) = a , 1/(y-2) = b then (1) and (2) becomes

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

=> b = 2-5a -------------------------(4)

and

6a-3b = 1 ---------------------------(5)

On substituting the value of b in (5) then

6a - 3(2-5a) = 1

=> 6a - 6 + 15a = 1

=> 6a+15a -6 = 1

=> 21a -6 = 1

=> 21a = 1+6

=>21 a = 7

=> a = 7/21

=> a = 1/3

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

=> 1(x-1) = 1×3

=> x-1 = 3

=> x = 3+1

=> x = 4

and

On substituting the value of a in (4)

b = 2-5(1/3)

=> b = 2-(5/3)

=> b = (6-5)/3

=> b = 1/3

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

=> (y-2) = 1×3

=> y-2 = 3

=> y = 3+2

=> y = 5

Therefore, x = 4 and y = 5

♦ Answer ♦ :-

• The solution of the pair of linear equations in two variables is (4 , 5)

♦ Check ♦ :-

If x = 4 and y = 5 then LHS of the equation (1)

[5/(x-1)] + [1/(y-2)]

=> 5/[(4)-1] + 1/[(5)-2]

=> 6/3

=> 2

LHS = RHS is true

and

If x = 4 and y = 5 then LHS of the equation (2)

[6/(x-1)] - [3/(y-2)]

=> 6/[(4-1)] -(3/3)

=> (6/3)-1

=> 2-1

=> 1

LHS = RHS is true

Hence, Verified.

♦ Used Method ♦ :-

• Reducing them to a pair of linear equations
• Substitution method

Step-by-step explanation:

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