Page 750 - Algebra 1

L E S S O N Graphing Systems of Linear Inequalities 109
Warm Up
New Concepts
1. Vocabulary A(n) (inequality, equality) is a mathematical
(45)
statement comparing quantities that are not equal. 2. Graph y < 2x + 3.
(97)
3. Is the boundary of the graph of y ≤ 3x + 5 solid or dashed? (97)
4. Is the shading above or below the boundary line on the graph (97) of y ≥ 2x - 6?
Recall that a system of linear equations is a set of two or more equations with the same variables.
The solution of the system below is (1, 2) because the ordered pair (1, 2) makes both equations true.
y=x+1 y = 2x
The coordinates also identify the point of intersection of the two lines.
y = x + 1 y = 2x
2 = 1 + 1 2 = 2(1) 2=2 2=2
y = x +
4
y
2
(1
, 2)
x
-4
1
-2
2
4
Likewise, a system of linear inequalities is a set of linear inequalities with the same variables.
In the system shown below, all of the ordered pairs in the overlapping region satisfy both inequalities. For example, (3, 2) lies in the overlapping region and makes both inequalities true.
y≤x+1 y ≤ 2x
A solution of a system of linear inequalities is an ordered pair or set of ordered pairs that satisfy all the inequalities in the system. Therefore, all the ordered pairs in the overlapping region make up the solution of the system.
y = 2x
-4
Math Reasoning
Verify Show that
(-4, -4) is not a solution of the system.
y
y ≤ x + 1 y ≤ 2x
2 ≤ 3 + 1 2 ≤ 2(3) 2≤4 2≤6
4
2
x
-4
-2
-4
2
olution set
4
s
Online Connection www.SaxonMathResources.com
Lesson 109 735