If it is not so then there will be triangular arbitrage. Learned in International Finances. As forex is almost perfect the triangular arbitrage happen very seldom. Or even does not happen. SO if Cross rate moves as moves its components then longing/shorting the cross is almost longing/shorting its components.
If you plan to go long at EURJPY you can went long in EURUSD and USDJPY at the same time. The profit/loss will be almost same. If it is not so then there is opportunity of riskfree profits. Called triangular Arbitrage
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