2/x+3/y=9/xy
4/x+9/y=21/xy,
wherex is not equal to 0 and y not equal to zero find the value of x and y
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Answer:
x = 1 and y = 3
Step-by-step explanation:
Given Equations :
- 2/x + 3/y = 9/xy
- 4/x + 9/y = 21/xy
On simplifying both the equations
⇒ 2/x + 3/y = 9/xy
⇒ ( 2/x + 3/y )xy = 9
⇒ 2y + 3x = 9 → ( 1 )
⇒ 4/x + 9/y = 21/xy
⇒ ( 4/x + 9/y ) = 21
⇒ 4y + 9x = 21 --- ( 2 )
LCM of coefficients of y is 4. So multiply ( 1 ) by 2
⇒ 2( 2y + 3x ) = 2( 9 )
⇒ 4y + 6x = 18 → ( 3 )
Subtracting ( 3 ) from ( 2 )
⇒ 4y + 9x - ( 4y +6x ) = 21 - 18
⇒ 3x = 3
⇒ x = 3/3 = 1
Substituting x = 1 in ( 1 )
⇒ 2y + 3x = 9
⇒ 2y + 3( 1 ) = 9
⇒ 2y + 3 = 9
⇒ 2y = 9 - 3
⇒ 2y = 6
⇒ y = 6/2 = 3
Hence the value of x is 1 and value of y is 3.
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