Absolute Value Equations and Inequalities

Solving systems of nonlinear equations relies on the same basic methods we used with linear ones: elimination and substitution. There are some extra considerations you have to keep in mind:

1. Graphing Helps You can't actually find the solutions just by graphing the equations but sketching a graph can help to confirm the number of solutions and their general values.
2. Systems Can Have No Solution These don't always look like the "false statements" like $0=3$ we saw before but they can also be "invalid" results like $x^2=-2$ when we're only looking for real solutions.
3. Systems Can Have Multiple Solutions
4. Checking Your Work Is Required Nonlinear systems are another example of a class of problem like radical equations where you can do everything right and still end up with solutions that don't work, i.e. what are called extraneous solutions. Checking your results is a requirement to make sure you catch these and eliminate them from your final result.