Question

Solve each of the following system of equations by elimination method.

Answer 1

3/x + 5/y = 20/xy

(3y + 5x)/xy = 20/xy

5x + 3y = 20------------( 1 )

2/x + 5/y = 15/xy

(2y + 5x)/xy = 15/xy

5x + 2y = 15---------------( 2 )

From-------( 1 ) & --------( 2 )

5x + 3y = 20
5x + 2y = 15
-------------------
Y = 5 [ put in ---( 1 )]


5x + 3(5) = 20

5x = 20 - 15

X = 5/5

X = 1 , y = 5


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Answer 2

GIVEN :
3/x + 5/y = 20/xy……………(1)
2/x + 5/y = 15/xy…………….(2)
Multiply eq 1 & 2 by xy on both sides
3 ×( xy) /x + 5×( xy)/y = 20 ×( xy)/xy
3y + 5x= 20
5x + 3y = 20 ………..,.( 1 )

2×( xy)/x + 5×( xy)/y = 15×( xy)/xy
2y + 5x = 15
5x + 2y = 15……………...( 2 )

On Subtracting eq 2 from 1
5x + 3y = 20
5x + 2y = 15
(-) (-) (-)
-------------------
y = 5

Put y = 5 in eq 1,
5x + 3y = 20
5x + 3(5) = 20
5x + 15 = 20
5x = 20 - 15
5x = 5
x= 5/5
x = 1

Hence, the value of x= 1 & y= 5.

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