焼く and 煮る: grilling and cooking in liquid
Choose the cooking verb according to the method, even for the same fish.
Grilling or baking
焼く (やく) describes cooking food with heat by grilling, baking, or similar methods. 「魚を焼きます」 says the speaker will grill fish.
「オーブンで肉を焼きました」 specifies an oven. Do not restrict 焼く to cooking over a direct flame.
Cooking in liquid
煮る (にる) describes cooking ingredients in water or seasoned liquid. 「魚を醤油で煮ます」 means simmering fish with soy sauce.
「弱火で煮てください」 requests cooking over low heat. The focus is cooking the ingredients, not simply the liquid boiling.
Different methods for one ingredient
「今日は焼かずに煮ます」 says that today the speaker will cook it in liquid instead of grilling it. 焼かずに excludes the grilling method.
「焼いた魚と煮た魚を比べました」 compares grilled fish with fish cooked in liquid. 焼いた and 煮た each modify the following 魚.
Does 「魚を焼かずに煮ました」 mean the fish was not cooked?
Show the answer and why
No. It was cooked in liquid, though not grilled. The negation applies specifically to 焼く.