If we were to mix two soluble salts together, for instance sodium nitrate and potassium chloride together, and their products are also soluble, will any reaction still occur? Say if we were to boil the solution, will we obtain only sodium chloride and potassium nitrate? Or will it be a mixture of all 4 possible salts.
Unless a precipitate forms from a double replacement reaction (basically cat$_1^+$an$_1^-$ + cat$^+$an$^-$ --> products), no reaction will occur from the dissolution of two salts. The precipitate can even be water, or a gas (like carbon dioxide, which will form from the decomposition of carbonic acid, alongside water).
e.g. H2SO4 + BaCl2 --> 2HCl + BaSO4 occurs because barium sulfate precipitates.
e.g. 2HNO3 + BaCl2 --> NO REACTION because neither hydrochloric acid nor barium nitrate precipitates. They just hang in the water as free ions (hence ionic equations).