Question

Solve the equation 2/x+3/y=30 and 5/8-4/y=-2 by reducing them 2a pair of Lenear equation

Answer 1

Answer :

x = 23/114 , y = 23/154

Solution :

Here ,

The given equations are ;

2/x + 3/y = 30

5/x - 4/y = -2

Putting 1/x = a and 1/y = b , the given equations will be reduced to linear equations .

2a + 3b = 30 ------(1)

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

Multiplying eq-(1) by 4 , we get ;

=> 4(2a + 3b) = 4•30

=> 8a + 12b = 120 --------(3)

Multiplying eq-(2) by 3 , we get ;

=> 3(5a - 4b) = 3•(-2)

=> 15a - 12b = -6 -------(4)

Now ,

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

=> 8a + 12b + 15a - 12b = 120 - 6

=> 23a = 114

=> a = 114/23

=> 1/x = 114/23

=> x = 23/114

Now ,

Putting a = 114/23 in eq-(1) , we get ;

=> 2a + 3b = 30

=> 2•(114/23) + 3b = 30

=> 228/23 + 3b = 30

=> 3b = 30 - 228/23

=> 3b = (690 - 228)/23

=> 3b = 462/23

=> b = 462/(23×3)

=> b = 154/23

=> 1/y = 154/23

=> y = 23/154

Hence ,

x = 23/114 , y = 23/154