Question

1/2x+1/3y=2 1/3x+1/2y=13/6 find the value of x and y

Answer 1

Step-by-step explanation:

• Suppose 1/x = a and 1/y = b

• so , a/2 + b/3 = 2 and a/3 + b/2 = 13/6

• After getting LCM we get equations as :-

° 3a + 2b = 12 ( LCM = 6 )

° 2a + 3b = 13 ( LCM = 6 )

Simplifying 1st equation

• 3a + 2b = 12

• 3a = 12 - 2b

• a = ( 12 - 2b )/3

Substituting value of a in 2nd equation

• 2a + 3b = 13

• 2( 12 - 2b )/3 + 3b = 13

• 2( 12 - 2b ) + 9b = 39 [LCM = 3]

• 24 - 4b + 9b = 39

• 5b = 15

• b = 3

• 3a + 2b = 12

• 3a + 2( 3 ) = 12

• 3a + 6 = 12

• 3a = 6

• a = 2

Now we have a and b so we can find x and y

• 1/x = a

• 1/x = 2

• x = 1/2

• 1/y = b

• 1/y = 3

• y = 1/3