Chapter: Linear Equations in Two Variables· Mathematics Part 1 (Algebra)
Answer: \(x = 3,\ y = 2\)
Put \(\dfrac{1}{x} = p\) and \(\dfrac{1}{y} = q\):
\(3p + 2q = 2\) …(I)
\(6p - 4q = 0\) …(II)
Multiply (I) by 2: \(6p + 4q = 4\) …(III)
(II) + (III): \(12p = 4 \Rightarrow p = \dfrac{1}{3}\)
From (II): \(4q = 6p = 2 \Rightarrow q = \dfrac{1}{2}\)
\(\therefore x = \dfrac{1}{p} = 3\), \(y = \dfrac{1}{q} = 2\).