Solve 6/x - 3/y = 2 and 4/x + 6/y = 4.

Step 1. Change letters. With $u = \dfrac{1}{x}$ and $v = \dfrac{1}{y}$, the pair is $6u - 3v = 2$ and $4u + 6v = 4$.

Step 2. Eliminate $v$. Multiply the first equation by $2$: $12u - 6v = 4$. Add the second equation: $16u = 8$, so $u = \dfrac{1}{2}$.

Step 3. Find $v$. $6 \times \dfrac{1}{2} - 3v = 2$ gives $v = \dfrac{1}{3}$.

Step 4. Change back. $x = \dfrac{1}{u} = 2$ and $y = \dfrac{1}{v} = 3$.