Download 7.6 Solving Systems of Linear Inequalities

Further preview of Sec
5.2.1
Objective: solve a
system of two linear inequalities in two
variables and to Graph the solution sets.
Warm Up
1. Determine whether the point P is a solution of
the linear inequality
y  2 x  1; P (2 , 2)
2. Solve the linear system (use any method).
3x + 4y = 5
-2x + y = 4
Quick Review
=
- What is the difference between an equation and
<,> an inequality? Which one is shaded? Inequality
- When is the line solid? ≤, ≥
- When is the line dashed (dotted)? <, >
- How do you figure out where to shade?
Pick a point to plug in.
Graph this inequality:
y>x–2
m=1
b = -2
Check if it’s a solution
1. (4, 10)
Check (4, 10)
9x – y ≥ 23
9x – y ≥ 23
5x + 0.2y ≥ 20 9(4) – 10 ≥ 23
36 – 10 ≥ 23
YES
26 ≥ 23 
2. (2, -1)
y ≤ 4x + 1
y > -x + 2
NO
5x + 0.2y ≥ 20
5(4) + 0.2(10) ≥ 20
20 + 2 ≥ 20
22 ≥ 20 
Check (2, -1)
y ≤ 4x + 1
-1 ≤ 4(2) + 1
-1 ≤ 8 + 1
-1 ≤ 9 
y > -x + 2
-1 > -(2) + 2
-1 > 0 
Graphing Systems of Linear
Inequalities
Graph each system
3. y < 2
x ≥ -1
4. y > x – 2
y≤-½x+3
Graphing Systems of Linear
Inequalities
Graph each system
5. y > 2x – 5
3x + 4y < 12
6. y ≥ -x + 2
2x + 4y < 4
Writing Systems of Linear Inequalities
Equation
Write the inequalities for each system
7.
8.
y4
1
y  x2
4
3
y x
2
y  2 x  4
Wrap Up
Checking solutions – have to work for both
equations
Graphing Inequalities
dashed (dotted) - < or >
solid - ≤ or ≥
shading – pick a point
Writing equations of inequalities
HW: P. 320 #19-23 odd, 29-43 odd
Write DLUQ for notes