1. 3.1 Graphing Systems of Equations
(Day 1)

2. 4 + 2 = 6
What could x and y be for this equation to be true?
Will any of the ordered pairs work for the second equation?
4 – 2 = 2
x y
Two or more linear systems together is called a system of linear equations. 6 1 5 2 4
The solution to this system is: 3 3 4 2 5 1

3. Same slope
Different y-intercepts
Same slope
Same y-intercepts
Different slopes
The lines intersect once so there is one solution.
The lines are parallel so there are no solutions.
The lines are the same line so there are infinitely many solutions.

4. Begin with b, move m 1=2(2) - 3 1= 2 - 1 (2, 1) Solve by graphing.
(more than once)
1=2(2) - 3
1= 2 - 1
(2, 1)
m is the slope
Note the characteristics!
b is the y intercept
Different slopes = one solution

5. White Boards (0, 3) Solve the system by graphing:
Check:
3 = 0 + 3
4(0) + 2(3) = 6
Note the characteristics!
Different slopes = one solution

6. White Boards No Solution Solve the system by graphing: Parallel Lines
Note the characteristics!
Same slopes
Different y-intercepts

7. Infinitely Many Solutions
Solve the system by graphing:
Slope-intercept
Remember: To graph a linear equation it must be in the y = mx + b form.
Same Line
Infinitely Many Solutions
Note the characteristics!
Same slopes
Infinitely Many
Same y-intercepts
Solutions

8. 3.1 Graphing Systems of Equations
(Day 2)

9. Different y-intercepts Same slope Same y-intercepts Different slopes
The lines intersect once so there is one solution.
The lines are parallel so there are no solutions.
The lines are the same line so there are infinitely many solutions.
Independent System
Inconsistent System
Dependent System
has a unique solution
has no solution
does not have a unique solution

10. The slopes are different and so the lines must cross only once…
Without graphing, classify the system as having one, none, or infinitely many solutions. List the slope and y-intercept of each line Is the system independent, dependent, or inconsistent?
The slopes are different and so the lines must cross only once…
One solution
Independent system

11. { y = 3x + 2 -6x + 2y = 4 y = 3x + 2 -6x + 2y = 4 2y = 6x + 4
Without graphing, classify the system as having one, none, or infinitely many solutions. List the slope and y-intercept of each line Is the system independent, dependent, or inconsistent? {
y = 3x + 2
-6x + 2y = 4
y = 3x x + 2y = 4
2y = 6x + 4
m = 3, b = m = 3, b = 2
Same m and b, so there is no unique solution:
Infinitely many solutions
dependent system 2.
Rewrite in slope-intercept form.
Find the slope and y-intercept.

12. { y = 4x + 3 -12x + 3y = 15 y = 4x + 3 -12x + 3y = 15 3y = 12x + 15
Without graphing, classify the system as having one, none, or infinitely many solutions. List the slope and y-intercept of each line Is the system independent, dependent, or inconsistent? {
y = 4x + 3
-12x + 3y = 15
y = 4x x + 3y = 15
3y = 12x + 15
y = 4x + 5
m = 4, b = m = 4, b = 5
Same m, different b:
no solution
inconsistent system 3.
Rewrite in slope-intercept form.
Find the slope and y-intercept.

13. One solution Independent system
Without graphing, classify the system as having one, none, or infinitely many solutions. List the slope and y-intercept of each line Is the system independent, dependent, or inconsistent?
White Boards
One solution
Independent system
No solution
Inconsistent system