Question

Solve the following systems of equations:
x + y = 5xy
x + 2y = 13xy, x ≠ 0, y ≠ 0

Answer 1

First,

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solution are (x,y)=(0,0)

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second,

now dividing both equation by xy

and multiply than adding we get,

the above mention result show in image

now supposing 1/x=a and 1/y=b

than by elimination method we will get another solution

a+b=5

2a+5b=13

b=1

1/y=1

y=1

so,

x=1/4

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solution are (x,y)=(1/4,1)

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Answer 2

First,

_________________

solution are (x,y)=(0,0)

_________________

second,

now dividing both equation by xy

and multiply than adding we get,

the above mention result show in image

now supposing 1/x=a and 1/y=b

than by elimination method we will get another solution

a+b=5

2a+5b=13

b=1

1/y=1

y=1

so,

x=1/4

__________________

solution are (x,y)=(1/4,1)

__________________