ようではないか is a literary and formal way to propose an action, often used in speeches, essays, or inspirational contexts. It carries a sense of urging or inviting a group (including the speaker) to act. In spoken Japanese, you'll almost always hear ましょう or しよう instead. The pattern is not used in casual conversation; it sounds like a rallying cry. It can be softened to ようじゃないか in slightly less formal speech, but that's still not casual. When answering or reacting, it's not a question expecting a literal answer—it's a call to action. Note that the よう here is not the same as the よう meaning 'appearance' or 'likeness'; it's the volitional form.