In this lesson, our instructor Vincent Selhorst-Jones teaches about Nonlinear Systems. Substitution, elimination, and graphing are covered in detail. Youll learn about shading appropriately, using dashed and solid lines, and how to clearly graph each inequality. The lesson ends with four practice problems.
A system of equations does not necessarily have to be linear (made up of straight lines only). Nonetheless, we can still use the methods we learned about in previous lessons.
Substitution is the most fundamental way to solve any system of equations: put one variable in terms of the other(s), then substitute and work to a solution.
In elimination, we add a multiple of one equation to the other to eliminate variables. In general, elimination is less useful for nonlinear systems. While it still works, it can be difficult to eliminate variables because the equations aren't
linear, so they don't match up as easily for cancellation.
We can also graph each equation in the system: wherever they intersect is a solution to the system. If you have a graphing calculator, you can use that to find the points of intersection for the system. [However, you will have to first put the equations
into a form that you can enter into your graphing calculator: y = .]
Unlike a linear system of equations, there can be any number of solutions. The only way to figure out how many solutions there are is by solving the system.
Working with nonlinear inequalities is very similar to working with linear inequalities:
Graph each inequality (as if they were equations);
Dashed < , > ; Solid: ≤ , ≥ ;
Shade appropriately (use test points to help).
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.