Question

Solve:

X+ 4y=27xy

X+2y=21xy

Answer 1

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