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Name: ____________________________________ Date: __________
Systems – Systems of Linear Inequalities Algebra I Common Core
1 Timmy’s Taco Truck sells tacos and burritos.
There are 15 people who work in your
department, so you need at least 15 items.
Write an inequality to represent the situation.
Graph the inequality on the axes below.
What do the points in the shaded region represent?
2 Timmy’s Taco Truck sells tacos for $2 each and
burritos for $5 each. You budget at most $50 to
spend at the truck for lunch for the office.
Write an inequality to represent the situation.
Graph the inequality on the axes below.
What do the points in the shaded region represent?
3 If both situations from problem 1 and problem 2 had to
be satisfied at the same time, we would graph both
situations on the same grid.
Where could we find the points that satisfy BOTH
situations?
Determine and state one combination of tacos and
burritos you can buy that will allow you to spend at
most $50 while buying at least 15 items.
Topic 6-3
Sheet #4
4 You cannot spend more than 30 minutes at the
gym today. You also need to burn off the 200
calorie piece of cake you ate with lunch today.
The stair master burns 8 calories per minute and
the row machine burns 6 calories per minute. The
graph below represents the situation.
Determine and state one combination of minutes that will
allow you to burn more than 200 calories while spending
less than 30 minutes at the gym.
5 Which ordered pair is in the solution set of the
system of linear inequalities graphed below?
(1) (1, -4)
(2) (-5, 7)
(3) (5, 3)
(4) (-7, -2)
6 What is one point that lies in the solution set of
the system of inequalities graphed below?
(1) (7, 0)
(2) (3, 0)
(3) (0, 7)
(4) (-3, 5)
7 Which ordered pair is in the solution set of the
following system of inequalities?
𝑦 <1
2𝑥 + 4
𝑦 ≥ −𝑥 + 1
(1) (-5, 3)
(2) (0, 4)
(3) (3, -5)
(4) (4, 0)
8 Which coordinates represent a point in the
solution set of the system of inequalities shown
below?
𝑦 ≤1
2𝑥 + 13
4𝑥 + 2𝑦 > 3
(1) (-4, 1)
(2) (-2, 2)
(3) (1, -4)
(4) (2, -2)
9 Which ordered pair is not in the solution set of
𝑦 < 2𝑥 + 2 and 𝑦 ≥ −𝑥 − 1?
(1) (10, 2)
(2) (-2, -7)
(3) (0, 0)
(4) (2, -1)
Name: ____________________________________ Date: __________
Systems – Systems of Linear Inequalities Algebra I Common Core
1 Which graph represents the solution of
𝑦 ≤ 𝑥 + 3 and 𝑦 ≥ −2𝑥 − 2?
(1)
(3)
(2)
(4)
2 Given: 𝑦 + 3𝑥 > 5
𝑦 ≤ 𝑥 + 2 Which graph shows the solution of the given
set of inequalities?
(1)
(3)
(2)
(4)
3 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
𝑥 + 2𝑦 < 4
c) The two inequalities graphed on the set of axes
form a system. Oscar thinks that the point (2,1) is
in the solution set for this system of inequalities.
Determine and sate whether you agree with Oscar.
Explain your reasoning.
Topic 6-3
Sheet #5
4 3𝑥 + 𝑦 < 7
𝑦 ≥2
3𝑥 − 4
State the coordinates of a point in the solution set.
5 𝑦 + 𝑥 ≥ 3
5𝑥 − 2𝑦 > 10
State the coordinates of one point that satisfies
𝑦 + 𝑥 ≥ 3, but does not satisfy 5𝑥 − 2𝑦 > 10.
Name: ____________________________________ Date: __________
Systems – Systems of Linear Inequalities Algebra I Common Core
1 The graphs of two linear equations are shown.
Replace the equal signs with inequality symbols to create a
system of linear inequalities, that has a point C as a solution, but
not points A, B, and D.
2 WHICH ONE DOESN’T BELONG? Use the graph shown. Which of the ordered pairs does not belong with the other
three? Explain your reasoning.
3
Topic 6-3
Sheet #6
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