Simultaneous Equations: Fraction Problem

There is a fraction. By letting the numerator be \(x\) and the denominator be \(y\), answer the following questions.

1. If \(4\) is added to the numerator and \(5\) is added to the denominator, the new fraction is equivalent to \(\frac{3}{4}\). Form an equation based on the information given and show that the equation reduces to \(4x-3y=-1\).
   
2. If \(1\) is subtracted from the numerator and the denominator is multiplied by \(4\) the new fraction is equivalent to \(\frac{1}{12}\). Form an equation based on the information given and show that the equation reduces to \(3x-y=3\).
   
3. Hence, solve the simultaneous linear equations and write down the original fraction.