Question

Solve each of the following systems of equations by the method of cross-multiplication :

`(ax)/b - (by)/a = a + b`

ax - by = 2ab

Answer 1

The given system of the equation may be written as

`a/b x xx - b/a xx y - (a + b) = 0`

ax - by - 2ab = 0

Here

`a_1 = a/b, b_1 = - b/a, c_1 = -(a + b)`

`=> x/(2b^2 - ab - b^2) = (-y)/(-2a^2 + a^2 + ab) = 1/(-a + b)`

`=>  x/(b^2 -ab) = (-y)/(-a^2 + ab) = 1/(-a + b)`               

`=> x/(b(b -a)) = (-y)/(a(-a + b)) = 1/(b - a)` 

Now

`x/(b(b - a))  = 1/(b -a)`                   

`=> x = (b(b -a ))/(b -a) = b`

And

`=> -y = (a(b - a))/(b -a)`

=> -y = a

=> y = -a

Hence, x = b, y = -a is the solution of the given system of equations.