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One narrow question per article, answered first — then the mechanism, an example, and the conditions under which it stops holding.
Why do bond prices fall when yields rise?
Higher yields usually mean lower fixed-rate bond prices, but the shortcut can fail when the yield or cash flows being compared are different.
Why does gold often rise when the dollar falls?
Gold is quoted in dollars, so a weaker dollar mechanically lifts the gold price — but the link is a tendency, not a rule, and it breaks in predictable ways.