Learn Swedish: Vi behöver byta diskmaskinen, men den nya är tyvärr för dyr. - We need to replace the dishwasher, but the new one is unfortunately too expensive.

You don't! Swedish doesn't use a placeholder word like "one". To refer back to a noun without repeating it, you just use the standalone definite article (den, det, or de) directly followed by the definite adjective (here, nya).

Why use den instead of det for "the" in the second half of the sentence?

The phrase den nya points back to diskmaskinen (the dishwasher). Since diskmaskin is an en-word, we must use the en-word article den. If we were replacing an ett-word like kylskåpet (the fridge), we would say det nya.

Why does nya end in -a if it describes a single dishwasher?

Adjectives get the -a ending in the plural, but also in the definite form. Because it follows the definite article den, nya must take this definite -a ending, even though the noun it describes is singular and omitted.

Doesn't byta mean "change" rather than "replace"?