Algebra b NAme: Unit 5: Solving systems of linear Equations Hourchoucairalgebra.weebly.com/uploads/7/8/1/7/78175388/unit_5_notes_notes.pdf · Solving systems of Equations BY substitution

Algebra b NAme: Unit 5: Solving systems of linear Equations Hour:

Date Section Homework

Wednesday January 9, 2019

Solving Systems of Equations by Graphing

p. 1 - 5

Homework 1: Solving Systems by Graphing

Thursday January 10, 2019

Review

Graphing Systems of Equations Review Partner Practice

Friday January 11, 2019

Solving Systems of Equations by Substitution (Day 1)

p. 6 - 7

Homework 2: Solving Systems by Substitution (Day 1)

Monday January 14, 2019

Solving Systems of Equations by Substitution (Day 2)

p. 8 - 9

Homework 3: Solving Systems by Substitution (Day 2)

Tuesday January 15, 2018

Review Graphing vs. Substitution “What do you get when you cross a Fish with an

Elephant?”


QUIZ


Solving Systems of Equations by Elimination (Day 1)

p. 10 - 12

Homework 4: Solving Systems by Elimination (Day 1)


Solving Systems of Equations by Elimination (Day 2)

p. 13 - 14

Homework 5: Solving Systems by Elimination (Day 2)


NO SCHOOL

Tuesday January 22, 2019

Review Elimination Maze Practice - Solving Systems by Elimination


SNOW DAY


QUIZ “Where do Snowmen keep their Money?”


Solving Systems of Equations All Types

Homework 6: Solving Systems (All Methods)


SNOW DAY Homework 7: Systems Word Problems

Tuesday January 29 , 2019

Systems of Equations Applications p. 15 - 17

Homework 7: Systems Word Problems

Wednesday - Monday January 30 to February 4

Practice Test &

Khan Academy

Study for Unit 5 TEST!

Tuesday February 5, 2019

TEST Study Guide, and Khan Academy DUE!

Solving systems of Equations BY GRAPHING

Content Objective: I can solve systems of linear equations in two variables graphically and algebraically. Language Objective: I can describe and explain in writing the graphic and algebraic solutions to systems of linear equations.

Main Idea ✎

SYSTEMS OF EQUATIONS

The SOLUTION to a System

Graphically: The point (x, y) where the two lines _______________ Algebraically: The point (x, y) that makes both equations __________

Types of Solutions

INTERSECTING LINES

PARALLEL LINES

SAME LINE

ONE SOLUTION NO SOLUTION INFINITE SOLUTIONS

1

EXAMPLES Write the system of equations and identify the solution.

1

System of Equations:

________________________________ ________________________________

Solution: ____________

2


________________________________ ________________________________

Solution: ____________

3 System of Equations:

________________________________ ________________________________

Solution: ____________

2

4 System of Equations:

________________________________ ________________________________

Solution: ____________

5


________________________________ ________________________________

Solution: ____________

6


________________________________ ________________________________

Solution: ____________

3

Solve a System by GRAPHING

EXAMPLES Solve the system of equations by graphing.

1. xy = 4 + 1 − xy = 2 − 5

2. xy = 25 + 8

− xy = 61 − 8

Solution: Solution:

3. y = x + 5 − xy = 3 − 7

4. xy = 43 + 8

− xy = 45 − 8

Solution: Solution:

4

5. xy = 31 + 2

x = 9

6. x y −2 − 3 = 3 −y = 3

Solution: Solution:

7. − xy = 2 + 2 x y 45 − 2 = 1

8. y 0x + 2 = 1 y −x − 4 = 8

Solution: Solution:

5

Solving systems of Equations BY substitution (Day 1)


Solving Systems by SUBSTITUTION

Steps to Solve

1. Look for an equation that is solved for x and y. 2. Substitute the expression into the other equation for that variable. 3. Solve! Now you have one variable. 4. Substitute your answer into either equation to find the other variable. 5. Write your answer as an ordered pair, (x, y).

EXAMPLES Solve the system of equations by substitution.

1. y = x − 9 x 4y = 4 − 2

2. − x 4y = 8 + 1 − x 1y = 5 + 1

6

3. x y− 5 + 4 = 7 − xy = 2 − 8

4. − x 3y = 4 − 2 x y 3− 4 − 3 = 1

5. −y = 4 x y 33 − 5 = 2

6. y = x − 8 x y 62 − 2 = 1

7. x y − 84 − 9 = 4 −x = 3

8. − x − y = 1 −y = x + 4

7

Solving systems of Equations BY substitution (Day 2)


Substitution that requires ISOLATION

The first step to solve system of equations by substitution is to look for an equation that is solved for x or y.

If there is not an equation, you will need to create one!

EXAMPLES Solve each system of equations using substitution.

1. x − 3 + y = 8 x y − 98 − 3 = 1

2. y − 6− x − 2 = 1 x4 + y = 1

3. x y −2 + 4 = 2 x5 − y = 6

4. x − 43 + y = 1 x y − 29 + 3 = 4

8

5. y − 8x + 2 = 1 x y 78 − 7 = 1

6. x y 03 + 2 = 2 y 2x − 7 = 2

7. x 2y −3 − 1 = 6 y −x − 4 = 8

8. y − 3x − 4 = 1 y 6x + 9 = 2

9. x y − 18 − 7 = 2 − 2x + y = 1

10. 1x − y = 1 y 9x − 4 = 2

9

Solving systems of Equations BY elimination (day 1)

Content Objective: I can solve systems of linear equations in two variables graphically and algebraically. Language Objective: I can describe and explain in writing the graphic and algebraic

solutions to systems of linear equations. Solving Systems by ELIMINATION

Steps to Solve

1. Make sure the equations are lined up! 2. Identify a variable that has the same coefficient on both equations. 3. Subtract the equations to eliminate this variable. 4. Solve the equation for the remaining variable. 5. Substitute your answer into either equation to find the other variable. 6. Write your answer as an ordered pair, (x, y). EXAMPLES Solve each system of equations using elimination.

1. x 3 y = 9 − 2 y = x + 1

2. − xy = 7 + 5 xy = 4 − 6

10

3. x 9y = 5 − 2 − x 9y = 7 + 1

4. − x 5y = 3 − 1 − xy = 2 − 8

5. x + y = 3 x − y = 7

6. x y − 17 − 4 = 1 x 0y 57 − 1 = 2

11

7. x y − 04 − 2 = 3 y− x − 2 = 5

8. x y − 55 + 2 = 2 x y − 84 + 2 = 1

9. x − 14 − y = 1 x − 67 − y = 2

10. x3 + y = 9 x −3 + y = 4

12

Solving systems of Equations BY elimination (day 2)


What if there are NO COMMON COEFFICIENTS?

EXAMPLES Solve each system of equations using elimination.

1. y x − 3 = 2 x y 74 + 7 = 2

2. x y − 27 − 2 = 3 y − 7x − 5 = 4

3. x y 92 − 5 = 3 x y 34 − 3 = 4

4. x − 64 + y = 1 x y − 73 + 2 = 1

13

5. x y − 4− 3 + 5 = 2 x 62 + y = 1

6. x y − 02 − 3 = 2 x − 37 − y = 1

7. x y2 + 3 = 1 x y −5 + 9 = 2

8. x y − 82 − 5 = 2 x − 86 − y = 2

14

Solving systems of Equations Applications


Many real world problems can be modeled and solved using a system of equations.

Use the process below to solve these problems.

15

16

17

Solving systems of linear inequalities

Content Objective: I can solve systems of linear inequalities in two variables. Language Objective: I can describe and explain in writing the graphic and algebraic solutions to systems of linear inequalities.

Main Idea ✎

SYSTEMS OF Linear Inequalities

SOLUTION to a System of

Linear Inequalities

ESSENTIAL UNDERSTANDING

You can graph the solutions of a system of linear inequalities in the coordinate plane. The graph of the system is the region where the graphs of the individual inequalities overlap.

LINES SHADING

18

EXAMPLES Solve the system of equations by graphing.

1. xy < 2 − 3 x2 + y > 2

2. xy < 2 + 4 x y− 3 − 2 ≥ 6

3. y > 5 xy < 2 − 3

4. xy > 41

−y ≤ x + 4

19

EXAMPLES Write a system of inequalities for each graph.

1

System of Inequalities:

________________________________ ________________________________

2


________________________________ ________________________________

3


________________________________ ________________________________

4


________________________________ ________________________________

20

21

Algebra b NAme: Unit 5: Solving systems of linear Equations Hourchoucairalgebra.weebly.com/uploads/7/8/1/7/78175388/unit_5_notes_notes.pdf · Solving systems of Equations BY substitution

Documents