Step 1: Link method to boiling point gap.
We separate two liquids by distillation. The right method depends on how far apart their boiling points are.
Step 2: Understand simple distillation.
Simple distillation works when the two boiling points are far apart (a large gap). The more volatile liquid boils off first and is collected, leaving the other behind.
Step 3: Understand fractional distillation.
Fractional distillation is used when the boiling points are close. A fractionating column gives many cycles of boiling and condensing, which separates the close-boiling liquids cleanly.
Step 4: Apply to mixture X.
Mixture X has a large difference in boiling points, so simple distillation is enough.
Step 5: Apply to mixture Y.
Mixture Y has only a small difference in boiling points, so we need fractional distillation.
Step 6: Write the pairing.
So X uses simple distillation and Y uses fractional distillation. \[ \boxed{\text{X: Simple distillation, Y: Fractional distillation}} \]