1. CHAPTER 3 LINEAR SYSTEMS
3.1 Solving Systems Using Graphs

2. SYSTEM OF EQUATIONS
 A system of equations is a set of two or more
equations
 A linear system consists of linear equations
 A solution of a system is a set of values for the
variables that makes all the equations true.
(usually an ordered pair)
 Systems can be solved be various methods: graphing,
substitution, and elimination

3. SOLVING A SYSTEM BY GRAPHING
1. Write each equation in slope-intercept form
2. Graph each line
3. Find the point of intersection (this is your solution)
4. Check by substituting the values into both
equations

4. SOLVE EACH SYSTEM BY GRAPHING

5. SOLVE EACH SYSTEM BY GRAPHING

6. CLASSIFYING SYSTEMS (PAGE 137)
 A system of two linear equations can be classified
by the number of solutions it has
 A consistent systems has at least one solution
 An independent system has one solution
 A dependent system has infinitely many solutions
 An inconsistent system has no solution

7. WITHOUT GRAPHING, CLASSIFY EACH SYSTEM AS
INDEPENDENT, DEPENDENT, OR INCONSISTENT
1. Rewrite each equation into slope-intercept form
2. Compare the slopes and y-intercepts
 Different slopes: independent system
 Same slope and same y-intercept: dependent system
 Same slope and different y-intercept: inconsistent

8. WITHOUT GRAPHING, CLASSIFY EACH SYSTEM AS
INDEPENDENT, DEPENDENT, OR INCONSISTENT

9. WITHOUT GRAPHING, CLASSIFY EACH SYSTEM AS
INDEPENDENT, DEPENDENT, OR INCONSISTENT

10. WITHOUT GRAPHING, CLASSIFY EACH SYSTEM AS
INDEPENDENT, DEPENDENT, OR INCONSISTENT

11. SYSTEMS OF LINEAR EQUATIONS AND THE
GRAPHING CALCULATOR
 Systems can be solved in the TI-83 or the TI-84
 This is useful to check your work.
 For the homework and test you will be expected to solve
a system by hand

12. ASSIGNMENT
 Page 138
 #7 – 9 use graphing calculator, sketch the graph in
your notebook
 The rest of the assignment must be done by hand
 #10 – 12, #17 – 37 odd