Can you hook up a washing machine to shower plumbing?

I was recently given a mobile home with two bathrooms. We would like to take out one of the bathtubs and put the washer and dryer where the tub was. We already have someone who can move the electrical/create a new dryer vent. My question is, can we hook the washer up to the pipes that were used for the shower? We are hoping to avoid hiring a plumber.