Transcript 9-28 Systems of Linear Inequalities

SYSTEMS OF LINEAR
INEQUALITIES
Solving Linear Systems of
Inequalities by Graphing
Solving Systems of Linear
Inequalities
1. We show the solution to a system of
linear inequalities by graphing
them.
a) This process is easier if we put the
inequalities into Slope-Intercept
Form, y = mx + b.
Solving Systems of Linear
Inequalities
2. Graph the line using the y-intercept
& slope.
a) If the inequality is < or >, make
the lines dotted.
b) If the inequality is < or >, make
the lines solid.
Solving Systems of Linear
Inequalities
3. The solution also includes points
not on the line, so you need to
shade the region of the graph:
above the line for ‘y >’ or ‘y ’.
b) below the line for ‘y <’ or ‘y ≤’.
a)
Solving Systems of Linear
Inequalities
Example:
a: 3x + 4y > - 4
b:
x + 2y < 2
Put in Slope-Intercept Form:
a)3x  4 y  4
b) x  2 y  2
4 y  3x  4
2 y   x  2
3
 y   x  1
4
1
 y   x  1
2
Solving Systems of Linear
Inequalities
Example, continued:
3
a : y   x  1
4
1
b : y   x  1
2
Graph each line, make dotted or solid
and shade the correct area.
a:
dotted
shade above
b:
dotted
shade below
Solving Systems of Linear
Inequalities
a: 3x + 4y > - 4
3
a : y   x  1
4
Solving Systems of Linear
Inequalities
a: 3x + 4y > - 4
b: x + 2y < 2
3
a : y   x  1
4
1
b : y   x  1
2
Solving Systems of Linear
Inequalities
a: 3x + 4y > - 4
b: x + 2y < 2
The area between the
green arrows is the
region of overlap and
thus the solution.
PRACTICE
#1 on Worksheet 3-2-2  We will
solve on the whiteboard together!
 STEP 1: REARRANGE inequalities to
look like y = mx + b
4x + 5y ≤ 2
y≤ x+3
-4x
-4x
(already done for you!)
5y ≤ -4x + 2
5
5 5
y ≤ -4/5x + 2/5

Practice (cont.)


STEP 2: Graph each inequality like a
linear equation.
STEP 3: Shade area where point values
“work” (plug in, does it make sense?)
Practice (cont.)


STEP 4: FIND THE COMMONLY
SHADED AREA.
STEP 5: This is your final answer (only
shade this part on final answer)
FINAL
ANSWER
PRACTICE (cont) (#2)
3x + 5y > 15
-3x
-3x
5y > -3x + 15
5
5
5
y > -3/5 x + 3
y≤ x–2
already done! 
Repeat graphing strategy (5 STEPS!)
PRACTICE

Solve # 3-8 on Worksheet 3-2-2 by
graphing on your whiteboard! 
(worksheet should be inside communicator!)