Definition: A System of Two Linear Equations in two variables x and y, also called a linear system, consists of two equations that can be written in the following form:
Dx + Ey = F Equation 2
A solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation.
In Algebra 2, there are three different ways to solve linear systems:
- Solve by Graphing
- Solve by Substitution
- Solve by Elimination
Here is a link to an applet used to graph and solve linear systems: Linear Systems Applet. The screen shot is here:
Here are some textbook “recipes” for solving linear systems by two of the three methods:
The Substitution Method
The Elimination Method
Here is a problem which requires applying the knowledge learned by solving linear systems. Note that this also addresses the area of multiple representations, discussed in Week 1.