Did you know that the GPS in your car or phone is a perfect example of a system of nonlinear equations?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Yep, the signal from multiple satellites positioned above the Earth, which form circular patterns, intersect each other to locate a single ordered pair, which determines your location.
And the way we find these points of intersection is exactly the same as how we solve linear systems of equations.
Wait!
Linear vs nonlinear, what’s the difference?
- Well, a linear equation is one where all the variables are to the power of 1 and its graph is a straight line.
- Whereas a nonlinear equation is when one or more variables in the equation are to a power other than 1 or there is a product of variables in one of the equations.
Now, solving systems of equations, regardless of it being linear or nonlinear, involves locating the point of intersection between two or three graphs. But with nonlinear systems, we may need to find more than one point of intersection.
And when we are asked to solve systems of nonlinear equations algebraically we will use the substitution method or the elimination method, or a combination of the two.
It is important to note that solving nonlinear systems predominately occurs in such courses as Algebra 2, Precalculus or above.
Why?
Because we will need to employ many of our solving skills, such as how to solve a polynomial equation, radical equation involving square roots, and we will also need to know how to handle both real and complex solutions.
And while only the real solution will represent the coordinates of the points where the graphs intersect, as Paul’s Online Notes so accurately states, it is important to be able to find all solutions, both real and complex.
Together we will look at seven questions in detail, and learn how to accurately solve systems of nonlinear equations.
Nonlinear Systems (How-To) – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.