Course: Algebra I / Elementary Algebra

Topic: Linear Systems

Subtopic: 2x2 Systems of Equations I - Graphically

**Overview**

When we studied lines, the equation was a single equation in two variables such as y=-2x+5. Today's lesson involves solving a __system of linear equations__ meaning that there are two or more equations to be solved simultaneously (at the same time). A 2x2 (read "two by two") system is two equations in two variables, a 3x3 system is three equations in three variables, etc. The solution to a 2x2 system is a point that lies at the intersection of the two lines in the system. So our goal today is to graph the lines in the system, find their intersection point, and that (x,y) is the solution to the system.

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 5.1.1 Know what it means to be a solution to a system of equations (algebraically and graphically)
- 5.1.2 Be able to check if given values are actually a solution to a given system
- 5.1.3 By observing a graph of a linear system, be able to identify if the system has no solution, one solution, or an infinite number of solutions
- 5.1.4 Solve a 2x2 linear system of equations by graphing manually
- 5.1.5 Solve a 2x2 linear system of equations by graphing electronically and using the grapher's intersection feature

**Terminology**

Define: linear, system, linear system of equations, consistent system (a single solution point), inconsistent system (no soluition), dependent system (an infinite number of solutions)

**Text Notes**

While working through the examples in the text try to make connections between the algebraic form of the system's equations, the graph of the lines, and the number of solutions.

**Supplementary Resources**

You must be able to use a calculator (handheld or software) to graph a system of two lines and find their intersection point (using the INTERSECTION feature of your grapher). If you have a handheld graphing calculator then these sites may help:

- For TI-84 (TI=Texas Instruments) see:

"Find the intersection of two graphs" video at Prof. Milner's Graphing Calculator Tutorials

- For TI-86, TI-89, or TI-92 see:

Prof. Keely's Calculator Guide: Intersection Points

- For other models (or makes) try searching on one of the sites recommended here: FAQs - Graphing Calculator Tutorials