Review of Linear
Inequalities
and
Systems of Linear
Inequalities
Use Desmos.com, Wabbit
and Graph paper to
understand graphs on .ppt
Review of Inequalities on Cartesian Grid
• Solid line as a boundary.
• Points above y=0.5x - 3 as
well as points on the line are
included in the solution set.
(x, y)
y ≥ 0.5x - 3
A(0,0)
(0) ≥ 0.5(0) - 3
0 ≥ -3
yes
B(2,-2)
(-2) ≥ 0.5(2) - 3
-2 ≥ -2
yes
C(10,0)
0 ≥ 0.5(10) - 3
0≥2
no
simplify true?
Review of Inequalities on Cartesian Grid
• Dashed line as a boundary.
• Points above y=0.5x - 3 but
not points on the line are
included in the solution set.
simplify true?
(x, y)
y > 0.5x - 3
A(0,0)
(0) > 0.5(0) - 3
0 > -3
yes
B(2,-2)
(-2) > 0.5(2) - 3
-2 > -2
no
C(10,0)
0 > 0.5(10) - 3
0>2
no
Inequalities on Cartesian Grid
Which of the following points
are in the solution set of
y > 0.5x – 3 and y > -x +3?
A(8,0), B(2,-1), C(5,2),
D(4,-1), E(3,-3)
simplify true?
(x, y)
y > 0.5x - 3
A(8,0)
(0) > 0.5(8) - 3
B(2,-1)
(-1) > 0.5(2) - 3 -1 > -2
y > -x + 3
true
for
simplify true? both?
no
(0) > -(8) + 3
0 > -5
yes
no
yes
(-1) > -(2) + 3
-1 > 1
no
no
C(5,2)
(2) > 0.5(5) - 3 2 > -0.5 yes
(2) > -(5) + 3
2 > -2
yes
yes
D(4,-1)
(-1) > 0.5(4) - 3 -1 > -1
(-1) > -(4) + 3 -1 > -1 yes
no
E(3,-3)
(-3) > 0.5(3) - 3 -3 > -1.5 no
0>1
no
(-3) > -(3) + 3
-3 > 0
no
no