Question

Solve the following pair of linear equations 1/2x +1/3y =3 and 2/x - 3/y) = - 1​

Answer 1

Answer :

x = 1/4 and y = 1/3

Solution :

Here ,

The given equations are ;

1/2x + 1/3y = 3

2/x - 3/y = -1

Putting 1/x = a and 1/y = b , the given equations will reduce to linear equations as follow ;

→ a/2 + b/3 = 3

→ (3a + 2b)/6 = 3

→ 3a + 2b = 3•6

→ 3a + 2b = 18 ------(1)

and

→ 2a - 3b = -1 ------(2)

Now ,

Multiplying eq-(1) by 3 , we get ;

=> 3•(3a + 2b) = 3•18

=> 9a + 6b = 54 -------(3)

Now ,

Multiplying eq-(2) by (2) , we get ;

=> 2•(2a - 3b) = 2•(-1)

=> 4a - 6b = -2 ------(4)

Now ,

Adding eq-(3) and (4) , we get ;

=> 9a + 6b + 4a - 6b = 54 + (-2)

=> 13a = 54 - 2

=> 13a = 52

=> a = 52/13

=> a = 4

=> 1/x = 4

=> x = 1/4

Now ,

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

=> 3a + 2b = 18

=> 3•4 + 2b = 18

=> 12 + 2b = 18

=> 2b = 18 - 12

=> 2b = 6

=> b = 6/2

=> b = 3

=> 1/y = 3

=> y = 1/3

Hence ,

x = 1/4 and y = 1/3 .