Looking at Special Systems of Equations

There are two sets of circumstances that provide interesting results when using systems of equations to solve for a variable. One situation provides us with a statement that looks like 0 = 10, which is obviously false. In cases like these, there will never be a time when the lines cross. This indicates that the lines are parallel (this can be verified by looking at the slopes of the lines). The answer to these types of problems in "no solution" or "no point of intersection".

In the second case, we will get a statement that looks like 0 = 0, which is always true. In these situations, graphing the equations will provide us with two lines sitting in the exact same place, meaning we've discovered two equations for the same line. These lines are called coincidental lines, and the answer for these types of problems will be "all real numbers".

Tonight's Homework: Lesson 7.5 ( 12 -28, even, 30, 36 )