You're buying two items, we can represent them as X. First you set one of the X's to be the dryer, and since we know that the washer costs 46 more than the dryer, that can be represented as X + 46. The equation can be written as follows:
x + (x + 46) = 696
2x + 46 = 696
2x = 650
x = 325
Therefore, the dryer costs $325, and the washer costs $371