3: Graphs and Equations with Two Variables

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In the previous unit we were able to solve a number of types of equations for the unknown. Sometimes there were no solutions, sometimes there was one solution and sometimes there were two. In all of these cases we were able to write down all of the solutions in a list.

In this unit we will be looking at equations with two variables. In this case, finding a solution involves specifying a value of each variable so that the equality after substituting in the values for the variables, respectively, is true. So a single solution involves specifying more than one number. Often it is the case that there are many more solutions, and in fact infinitely many, so that writing them in a list would be impossible! We therefore will devise here a way of illustrating the solutions.