The document contains notes from a math lesson on solving systems of linear equations and inequalities. It includes examples of solving systems by graphing the lines on a coordinate plane to determine the number of solutions. Systems can have one solution, no solution, or infinitely many solutions depending on whether the lines intersect at a point, are parallel, or are the same line. The lesson examples graph systems of equations and identify the number of solutions each system has.

1. Lesson 6­1.notebook January 17, 2013
Assignment:
1­­>L6.1, pg. 336­337, #16 ­ 24 (evens) & #28 ­ 40 (evens) ­ Due Wednesday (1/23)
2­­>L6.2, pg. 345, #2­22 (evens) ­ due Wednesday (1/23)
3­­>Chapter 5 Test signed for extra credit??

2. Lesson 6­1.notebook January 17, 2013
Lesson 6.1 WarmUp:
Solve each inequality.
1) ­2x + 4 > ­6
2) 5n ­ 3(n ­ 6) > 0
3) 23 ­ t < 2(t ­ 9) ­ 3(t + 2)
Solve each compound inequality. Then graph the solution on a number line.
4) m + 3 > 5 and m + 3 < 7
5) ­n > 2 or 2n ­ 3 > 5

3. Lesson 6­1.notebook January 17, 2013
Lesson 6.1:
*FYI...the solution for a system of equations is the ordered pair that is a solution
for all of the equations....
...and..system of equations can have one solution, an infinite number of
solutions, or no solutions....
**IF the system has one solution, it is called consistent. [the graphs intersect
at one point or are the same line]
***IF the consistent system has EXACTLY one solution, it is called
independent. [the graphs intersect at exactly one point]
****IF the consistent system has an INFINITE number of solutions, it is called
dependent. [the graphs are the same line(s)]

4. Lesson 6­1.notebook January 17, 2013
*****IF the system has no solution, it is called inconsistent. [the
graphs are parallel]
­­>Look at the Concept Summary chart on page 333 in your
book!
ONE way to solve a system of linear
equation is to GRAPH them!

5. Lesson 6­1.notebook January 17, 2013
Lesson 6.1 examples:
Graph each system and determine the number of solutions it has. If it
has one solution, name it.
A) y = 2x + 3
y = ­2x + 3 Y
X

6. Lesson 6­1.notebook January 17, 2013
B) y = ­3x + 10 Y
y = x ­ 2
X

7. Lesson 6­1.notebook January 17, 2013
C) x + y = 4 Y
3x + 3y = 12
X

8. Lesson 6­1.notebook January 17, 2013
D) 2x ­ y = ­1
4x ­ 2y = 6 Y
X

9. Lesson 6­1.notebook January 17, 2013
E) x + 2y = 3 Y
x = 5
X