Download Regents Review 6 - Solving Linear and Systems of Inequalities

Name:_____________________________
Common Core Algebra 10A—Ms. Contrada
Regents Review
Topic #6:
Graphing Linear & Systems of Inequalities
Graph y - 2x ≤ 3
Step 1: Solve the inequality for ‘y’ first!
Step 2: Graph the inequality just like you graph
a linear equation by identifying the slope (m) and
y-intercept (b)
Step 3: Connect the points to form
the dotted/solid line.
Step 4: Choose a test point (usually (0,0)) to
determine which side of the boundary line to
shade for the solution set.
Step 5: Label the graph with
the original inequality.
a) Is (5, 1) a solution to inequality?
b) Is (-7, 4) a solution to the inequality?
What We Need To Know When Graphing Inequalities:
Graph
y < 2x + 4
Step 1: Solve the inequality for “y” first!
-3x - 2y ≥ 6
Step 2: Graph the inequality just like
you graph a linear equation by
identifying the slope(m) and
y-intercept (b)
Step 3: Connect the points to form
the dotted / solid line.
REMINDER:
 
≤ or ≥
 solid line
< or >
 dashed line
Step 4: Choose a test point to
determine which side of the boundary
line to shade for the solution set.
Step 5: Label the graph with the
original inequality.
Step 6: Repeat steps #1-5 to graph the
second inequality
Step 7: Located where the shading overlaps.
Label the solution set with a bold “S”
a)
Name a few points that are a solution to this system: ______________________________
b)
Name a few points that are not solutions to this system:_____________________________
1. Which of the following point’s lies in the solution set of the system of inequalities shown graphed
below?
(1) (1, 0)
(3) (2, 2)
(2) (-4, 0)
(4) (2, -4)
2. Would the point (5, 10) lie in the solution set of the system of inequalities shown below? Justify your
answer.
x2
y  3x  7
3. Which ordered pair is not in the solution set of y  
(1) (5, 3)
(3) (3, 4)
(2) (4, 3)
(4) (4, 4)
1
x  5 and y  3x  2 ?
2
4. Given y  3  2 and y  3x  2 , which graph shows the solution to the given set of inequalities?
(1)
(3)
(2)
(4)
5. The graph of an inequality is shown below.
a) Write the inequality represented by the graph.
b) On the same set of axes, graph the inequality 2 + y > x.
c) The two inequalities graphed on the set of axes form a system. Michelle thinks that the point (3, 1) is
in the solution set for the system of inequalities. Determine and state whether you agree with Michelle.
Explain your reasoning.
6. The graph of an inequality is shown below.
a) Write the inequality represented by the graph.
b) On the same set of axes, graph the inequality -2 + y > -x.
c) The two inequalities graphed on the set of axes form a system. Aidan thinks that the point (0, 2) is in
the solution set for the system of inequalities. Determine and state whether you agree with Aidan.
Explain your reasoning.
7. The sum of x and y is less than or equal to 5. When multiply 4 and y, it is greater than x. Graph the
inequalities that represent this scenario on the set of axes below.
Maggie says the point (4, 1) is a solution to this system. Determine if she is correct and explain your
reasoning.
8. The sum of two numbers, x and y, is more than 8. When you double x and add it to y, the sum is less
than 14. Graph the inequalities that represent this scenario on the set of axes below.
Name a point in the solution set. Justify your solution.
9. Suppose you can work a total of no more than 20 hours per week at your two jobs. Baby-sitting pays
$15 per hour and your cashier job pays $10 per hour. You want to earn at least $150 a week to save up
to buy a car.
a. Write a system of inequalities that can be used to represent the situation.
b. On the set of axes below, graph these inequalities.
c. Determine a combination of hours that will allow you to earn at least $150 per week while working no
more than 20 hours.
10. A local cinema is conducting a mathematical study. In its theater, there are 200 seats. Adult tickets
cost $12.50 and child tickets cost $6.25. The cinema's goal is to sell at least $1500 worth of tickets for
the theater.
Write a system of linear inequalities that can be used to find the possible combinations of adult tickets,
x, and child tickets, y, that would satisfy the cinema's goal.
Graph the solution to this system of inequalities on the set of axes below. Label the solution with an S.
Matt claims that selling 30 adult tickets and 80 child tickets will result in meeting the cinema's goal.
Explain whether he is correct or incorrect, based on the graph drawn.