This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow simple and elegant solutions to seemingly complex problems. The trick is to find the basic mathematical idea that can be used to simplify the task. Initially, many students use what the authors call the "graffiti" method, which, although correct, usually creates a much more complex problem than that initially posed. With practice and experience, however, students surprise them as well as themselves by using what the authors refer to as the "calligraphy" method. As defined by Webster's online dictionary, "graffiti" is "a rude decoration inscribed on rocks or walls," and "calligraphy" is "the art of elegant handwriting. The use of these terms in mathematics classes refers to the differences between equally correct but distinguishable techniques in problem solving; both require work and training, but of a different kind. The authors state that they tell students that they have used the "graffiti" method when they have arrived at the correct answer or solution to a problem by performing unnecessary steps and sometimes by over-complicating their thinking process. However, in noting that the "graffiti" method often creates a much more complex problem, they advise their students to use the "calligraphy" method.