This document discusses how to graph and solve systems of linear equations in two variables by determining whether the system has one solution, many solutions, or no solution. It explains that a consistent system has a solution, an inconsistent system has no solution, an independent system has one solution, and a dependent system has infinitely many solutions. It also notes that a system will have one solution if the lines cross once, no solution if the lines are parallel, and infinitely many solutions if the lines are the same.

1. 3.1A SOLVING Systems of Linear
Equations BY GRAPHING
Today’s objective:
1. I will graph and solve systems of
linear equations in two variables with
one solution, many solutions, or no
solution.

2. Is there a solution to the
system?
 If there is a solution, the system is called
consistent.
 If there is not a solution, the system is
called inconsistent.

3. How many solutions to the system?
 If there is only one solution, the system is
called independent.
 If there are infinitely many solutions, the
system is called dependent.

4. •If the lines cross once, there
will be one solution.
( Consistent & Independent)
•If the lines are parallel, there
will be no solutions.
(Inconsistent)
•If the lines are the same, there
will be an infinite number of solutions.
(Consistent & Dependent)