Question

can anyone intelligent student can help in mathematics tomorrow is my board exam and i need someone help ( please give your wo number )​

Answer 1

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Question

Solve:

X+ 4y=27xy

X+2y=21xy

Solution

x + 4y = 27xy -------- 1)

x + 2y = 21xy --------2)

we know that we can't solve these two equations by having the xy term on the RHS. So we have to remove it by some or other way. Here if we divide both the equations by xy then we can remove xy from RHS.

(x /xy+ 4y/xy = 27xy) /xy

x/xy + 4y/xy = 27/xy

1/y + 4/x = 27

1(1/y) + 4(1/x) = 27

We will substitute 1/x with q and 1/y with p

p + 4 q = 27

x/xy + 2y/xy = 21xy/xy

1/y + 2/x =21

1(1/y) + 2(1/x) = 21

p + 2q = 21

Using elimination method

p + 4q = 27

-

p+ 2q = 21

2q = 6

q = 3

p + 2q = 21

p+ 2(3) =21

p + 6 = 21

p = 15

1/y = p

1/y = 15

15y = 1

y = 1/15

1/x = q

1/x = 3

3x =1

x = 1/3

Hope you got it

alternative to fing value of X

simply subtract the equations

we get

2y=6xy

or

y=3xy

y-3xy=0

y(1-3x)=0

that is y=0 or 1-3x =0

that is x=1/3

but when x=1/3,then y is not equal to zero

but good method to find values of both x and y is above