When any two curves are graphed on the same coordinate plane, any one of three following situations may occur.

* The curves intersect in a finite number of points.

* The curves do not intersect in any points.

* The curves coincide as one curve and intersect as an infinite number of points.

Whether two or more curves intersect or not, is an important topic in mathematics and leads to a study of matrices to determine if a set of problems contains multiple solutions. Over the next few units, we will examine techniques to find solutions to a “System of Equations”. At first, we will examine algebraic and graphing techniques. Later we’ll examine matrix algebra to find our answers.

A “system of equations” consists of one or more equations in one or more variables such that the solutions to each equation result in a solution to the system.

In previous mathematics courses, you learned three methods to find a solution to a system of equations. These methods are (1) Method of Variable (or quantity) Substitution, (2) Method of Elimination of Variables, and (3) Graphing methods.

In this unit we will review the first two methods briefly, and then examine graphing methods on the TI-83+ Graphing Calculator.

Solving systems of linear equations — Basic example (video) | Khan Academy

Systems of equations with substitution: -3x-4y=-2 & y=2x-5 (video) | Khan Academy

Systems of Equations with More Than Two Variables

Linear and Quadratic Equations--Skydiving (02:37)

Below are additional educational resources and activities for this unit.

Solving Systems of Three Equations w/ Substitution

Solving Systems of Three Equations w/ Elimination