Form the pair of linear equations for the following problems:
(i) The difference between two numbers is \(25\) and one number is 3 times the other. The equation for the given situation is and
(ii) A fraction becomes \(\frac{9}{11}\), if \(2\) is added to both the numerator and the denominator. If, \(3\) is added to both the numerator and the denominator it becomes \(\frac{5}{6}\). The equation for the given situation is and
(iii) The age of the mother is twice the sum of the ages of his two children. After \(20\) years, his age will be equal to the sum of the ages of his children. The equation for the given situation is and
(iv) The sum of a two-digit number and the number obtained by reversing the digits is \(66\). If the digits of the number differ by \(2\). The equation for the given situation is and
(v) A two-digit number is obtained by either mutliplying the sum of the digits by \(8\) and then subtracting \(5\) or by multiplying the difference of the digits by \(16\) and then adding \(3\). The equation for the given situation is and
Answer variants:
\(6x-17y=-3\)
\(11x-9y=-4\)
\(x+y=6\)
\(y-x=25\)
\(x-y=2\)
\(2x-7y=-5\)
\(x=2y\)
\(6x-5y=-3\)
\(x-y=20\)
\(y=3x\)