WARM UPSolve the following systems of linear equations by any method of your choice.

1. 2.

Infinitely many solutions

No solution

HOMEWORK ANSWERS12. E; exactly one solution

13. D; no solution

14. F; exactly one solution

15. B; infinitely many solutions

16. A; no solution

17. C; infinitely many solutions

18. no solution

19. infinitely many solutions

20. exactly one solution; (0, -4)

21. infinitely many solutions

22. one solution; (-1, -4)

23. no solution

7.6 –

GRAPHING

SYSTEM

S OF

LINEA

R

INEQ

UALITI

ES

AL

GE

BR

A 1

( B)

OBJECTIVES

1. Graph systems of linear inequalities

2. Apply systems of linear inequalities in a real-world context

SYSTEMS OF INEQUALITIES

Solution of a Linear System of Equations

• Can be determined by graphing, combination, or substitution

• Written as an ordered pair

• Point of intersection of two lines

• Makes all equations in the system true

Solution of a Linear System of Inequalities

Brainstorm with a partner: What does is mean to be a solution of a linear system of equations?

SYSTEMS OF INEQUALITIES

System of Linear Equations

{2𝑥+3 𝑦=18

𝑦=23𝑥+2

System of Linear Inequalities

{2𝑥+3 𝑦 ≤18

𝑦>23𝑥+2

Systems of linear inequalities have inequality symbols:

Less thanLess than or

equal to Greater than

Greater than or equal to

SYSTEMS OF INEQUALITIES

Solve the system of inequalities by graphing.

{2𝑥+3 𝑦 ≤18

𝑦>23𝑥+2

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

Steps:1. Graph both inequalities (pretend

they are equations).

2. Determine whether the lines should be solid (, ) or dashed (, ).

3. Use test point (usually ) to determine shading.

4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!

5. Check a solution in the double-shaded region!

SYSTEMS OF INEQUALITIES

Solve the system of inequalities by graphing.

{ 𝑦<2𝑥≥−1𝑦>𝑥−2

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

Steps:1. Graph both inequalities (pretend they

are equations).

2. Determine whether the lines should be solid (, ) or dashed (, ).

3. Use test point (usually to determine shading.

4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!

5. Check a solution in the double-shaded region!

BREAK TIMEUse this time to get up, stretch out, talk to a neighbor, or try the following rebus puzzles…

Beaten black and blue

To err on the right side

SYSTEMS OF INEQUALITIES

Solve the system of inequalities by graphing.

{𝑦<3𝑦 >1

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

Steps:1. Graph both inequalities (pretend they are

equations).

2. Determine whether the lines should be solid (, ) or dashed (, ).

3. Use test point (usually to determine shading.

4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!

5. Check a solution in the double-shaded region!

SYSTEMS OF INEQUALITIES

Solve the system of inequalities by graphing.

{ 𝑦 ≥ 𝑥−2−𝑥+𝑦<1

1 2 3 4 5 6 7 8 9 10

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

Steps:1. Graph both inequalities (pretend they are

equations).

2. Determine whether the lines should be solid (, ) or dashed (, ).

3. Use test point (usually to determine shading.

4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!

5. Check a solution in the double-shaded region!

SYSTEMS OF INEQUALITIES

Solve the system of inequalities by graphing.

{𝑦+1≥ 23𝑥

𝑦<4 𝑥+11 2 3 4 5 6 7 8 9 1

0

123

56

4

789

10

-6-4 -2-8

-6

-2

-4

-8

Steps:1. Graph both inequalities (pretend they are

equations).

2. Determine whether the lines should be solid (, ) or dashed (, ).

3. Use test point (usually to determine shading.

4. Find overlap in shading. THESE ARE YOUR SOLUTIONS!

5. Check a solution in the double-shaded region!

EXIT SLIP• Complete the exit slip individually

before leaving today

• You may use your notes or textbook if you want

• When you are done, you may begin the homework assignment

HOMEWORKDo the following four problems on graph paper by tomorrow!

1. 2. 3.

Graph the system of linear inequalities. Show your work!

4.