Question

Solve the following pair of equation's by reducing to a pair Linear's equation (i) 2/x + 3y = 13 and (ii) 5/x - 4/y = 2

Answer 1

Question:

Solve the given pair of equations by reducing to a pair Linear equations :-

2/x + 3y = 13

5/x - 4/y = - 2

Answer:

x = 1/2 , y = 1/3

Solution:

Here,

The given pair of equations are :-

2/x + 3y = 13 ---------(1)

5/x - 4/y = - 2 ---------(2)

Now,

Let 1/x = a and 1/y = b.

Also,

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

They will reduced to linear equations.

2a + 3b = 13 -------(3)

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

Now,

Multiplying both sides of eq-(3) by 4 , we get ;

=> 4•(2a + 3b) = 4•13

=> 8a + 12b = 52 --------(5)

Also,

Multiplying both sides of eq-(4) by 3 , we get ;

=> 3•(5a - 4b) = 3•(-2)

=> 15a - 12b = - 6 ---------(6)

Now,

Adding eq-(5) and eq-(6) , we get ;

=> 8a + 12b + 15a - 12b = 52 - 6

=> 23a = 46

=> a = 46/23

=> a = 2

=> 1/x = 2

=> x = 1/2

Now,

Putting a = 2 , in eq-(3) , we get ;

=> 2a + 3b = 13

=> 2•2 + 3b = 13

=> 4 + 3b = 13

=> 3b = 13 - 4

=> 3b = 9

=> b = 9/3

=> b = 3

=> 1/y = 3

=> y = 1/3

Hence,

The solution of the given pair of equations is :

x = 1/2 , y = 1/3

Answer 2

Correct Question :-- Solve the following pair of equation's by reducing to a pair Linear's equation (i) 2/x + 3/y = 13 and (ii) 5/x - 4/y = 2 ..

Solution:

Given Equations Reducible to a Pair of Linear Equations in two variables :

→ 2/x + 3/y = 13 ------------- Equation (1)

→ 5/x - 4/y = (-2) ------------- Equation (2)

substituting 1/x = a and 1/y = b , we get the following pair of linear equations:

→ 2a+3b=13 -------------- Equation (3)

→ 5a-4b = (-2) --------------Equation (4)

Coefficients of b are 3 and 4 and their LCM is 12 .

Using the elimination method .

→ 8a+12b = 52 (Equation (3) × 4) ------- Equation (5)

→ 15a-12b= (-6) (Equation (4) × 3) ------- Equation (6)

'b' terms have opposite sign , so adding Equation (5) and (6) we get :----

=> 23a = 46

Divide both sides by 23

=> a = 46/23

=> a = 2

Substitute the value of a in equation (3), we get :--

=> 2×2 +3b = 13

=> 4 + 3b = 13

=> 3b = 13 - 4

=> 3b = 9

=> b = 9/3

=> b = 3

Now, putting both Equal to substituting values we get,

1/x = a = 2

x = 1/2

and,

1/y = b = 3

y = 1/3

Hence, value of x is 1/2 and y is 1/3 .......