HW #29: p. 148 (1-19)
Aim #30: How do we solve a system of inequalities graphically?
Homework: Handout
Do Now: Consider the system of inequalities below:
x + y > 10
y ≤ 2x + 1
a) Does the point (4, 7) make the inequality x + y > 10 true?
b) Does the point (4, 7) make the inequality y ≤ 2x + 1 true?
c) Based on your answers from parts a and b would (4, 7) be a solution to the system
of inequalities?
Now, let's solve the system of inequalities graphically.
x + y > 10
y ≤ 2x + 1
a) Represent the solution to this system
graphically.
b) Name a point that is a solution to
x + y > 10 but not y ≤ 2x + 1.
c) Name a point that is a solution to y ≤ 2x + 1 but not x + y > 10.
d) Name a point that is a solution to both inequalities.
e) Where does the solution to a system of inequalities lie?
1) Solve each system of inequalities graphically.
a)
c)
y > 4x - 1
2y < -x + 16
2x - y < 3
4x + 3y ≥ 0
b)
d)
3x + y ≤ 5
3x + y ≥ 8
x-y>5
x > -1
e)
x+y>2
y≤x
f)
2) Consider the compound sentence below.
x + y > 10 and y = 2x + 1
a) Graph the solution set to both x + y > 10
and y = 2x + 1.
b) Describe the solution set to x + y > 10
and y = 2x + 1.
1
y<1
4
4x + 8y > 16
2x -
3) Given: y + x > 2
y ≤ 3x - 2
Which graph shows the solution of the given set of inequalities?
4) State if each point is a solution to the system of inequalities illustrated in the
graph below.
a) (7, 0)
yes
b) (3, 0)
no
c) (0, 7)
no
d) (6, -7)
yes
Sum it Up!
The solution to a system of inequalities can be found on a graph by identifying where the
overlaps
shading _______________.