Question

solve the following equation by reducing them to a pair of linear equations:​

Answer 1

Step-by-step explanation:

Given :-

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

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

To find :-

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

Solution :-

Given equations are :-

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

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

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

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

On multiplying with 3 then

15a + 3b = 6 -----------(4)

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

On subtracting (5) from (4)

15a + 3b = 6

6a +3b = 1

(-)

__________

9a + 0 = 5

___________

=> 9a = 5

=> a = 5/9

On Substituting the value of a in (5)

6(5/9)+3b = 1

=> 2(5/3)+3b = 1

=> (10/3)+3b = 1

=>3b = 1-(10/3)

=> 3b = (3-10)/3

=> 3b = -7/3

=> b = -7/(3×3)

=> b = -7/9

We have ,

a = 5/9

=> 1/(x-1) = 5/9

=> x-1 = 9/5

=> x = (9/5)+1

=> x = (9+5)/5

=> x = 14/5

and

b = -7/9

=> 1/(y-2) = -7/9

=> y-2 = -9/7

=> y = (-9/7)+2

=> y = (-9+14)/7

=> y = 5/7

Therefore , x = 14/5 and y = 5/7

Solution :-

The solution for the given problem is (14/5 , 5/7)

Check :-

x = 14/5 and y = 5/7

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

=> 5/[(14/5)-1] + 1/[(5/7)-2]

=>5/(9/5) + 1/(-9/7)

=> (25/9)-(7/9)

=> (25-7)/9

=> 18/9

=> 2

LHS = RHS

and

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

=> 6/[(14/5)-1)] +3/[(5/7)-2]

=> 6/(9/5)+ 3/(-9/7)

=> (30/9)-(21/9)

=> (30-21)/9

=> 9/9

= 1

LHS = RHS is true for x = 14/5 and y = 5/7

Used Method :-

• Reducing them to a pair of linear equations

• Elimination method