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Question

Solve the following equations for (x,y).

2x+y3x−y−x−yx+y=2815,
7x+5y=29

A
(1,2)
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B
(2,3)
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C
(2,3)
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D
(4,2)
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Solution

The correct option is A (2,3)
Given equations are 2x+y3xyxyx+y=2815 ..........(1)
and 7x+5y=29 ...........(2)
(2x+y)(x+y)(3xy)(xy)(3xy)(x+y)=3815
2x2+2xy+xy+y23x2+3xy+xyy23x2+3xyxyy2=3815
x2+7xy3x2+2xyy2=3815
15x2+105xy=114x2+76xy38y2
129x229xy38y2=0
129x286xy+57xy38y2=043x(3x2y)+19y(3x2y)=0
(43x+19y)(3x2y)=0
43x+19y=0 ........(3)
3x2y=0 ..........(4)
Solving (2) and (3), we get
From (3) y=43x19
Substituting in (2), we get
7x+5(43x19)=29x=58182
Substituting back in (2) y=124782
So, (58182,124782) is one solution of the equation
Similarly by solving (2) and (4), we get
x=2 and y=3
So, (2,3) is the other solution of the given equations.

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