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