Dr. Fraser introduces this new section on Systems of Equations with the most intuitive way of solving. You will learn how to solve systems of equations by graphing and finding the points of intersection. You will also cover the different cases and number of solutions which will range from independent to dependent and inconsistent. In mathematics, the theory of linear systems is a branch of linear algebra, a subject which is fundamental to modern mathematics Four examples round out this first lecture.
A system of
equations is two equations in two variables. A solution
consists of values for each unknown that satisfy both equations.
A system can have
one, infinite, or no solutions.
The system is
called independent if it has one solution. In this case, the
graphs of the two equations intersect at one point.
It is called
dependent if it has infinitely many solutions. In this case,
the graphs are the same line.
It is called
inconsistent if it has no solution. In this case, the graphs
You can solve a
system by graphing. Always check your solutions to be sure you have
read the graph accurately.
Use the method of
graphing when you are willing to settle for an estimate for the
Graphing Systems of Equations
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.