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Question
Solve each of the following systems of equations by the method of cross-multiplication :
`(ax)/b - (by)/a = a + b`
ax - by = 2ab
Solution
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.
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