bell work 2/11/2015 solve the system by substitution

Bell Work 2/11/2015

31.

2 4 6

x

x y

Solve the system by substitution.

2 4 6x y 2 4 6y 3

6 6

3y

3, 3

6 4 6y

4 44 12y

22.

3 4 10

y x

x y

3 4 10x y 3 4 10x 2x

2x 2, 4

3 8 10x x

5 55 10x

2y x 2y 2

4y

Yesterday’s Homework

1. Any questions?2. Please pass your homework to the front.

• Make sure the correct heading is on your paper.• Is your NAME on your paper?

• Make sure the homework is 100% complete.• Incomplete work will NOT be accepted.

Solving Systems by Elimination (opposites)

04/20/23

Heading

TSWBAT: solve a linear system by elimination when already having opposites.

Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

6.3A

Notes• Solving a System by Elimination

1. Arrange the like variables in columns.

- This is already done.

2. Pick a variable, x or y, and make the two equations opposites using multiplication.

3. Add the equations together (eliminating a variable) and solve for the remaining variable.

4. Substitute the answer into one of the ORIGINAL equations and solve.

5. Check your solution.

Notes

2 5

2 3 7

x y

x y

Ex.

Solve the system by linear combination.

2) Make opposites.

3) Add and solve for the variable.

4) Substitute into ANY original equation.

1) Arrange the variables.

3y

1, 35) Check your answer.

4 12y 4 4

2 5x y 2 5x 3

3 3 2 2x 2 2

1x

Notes

2 5

2 3 7

x y

x y

Ex.


2) Make opposites.




5) Check your answer.

2 5x y 2 5 1 3

2 3 5

Check

5 5

2 3 7x y 2 3 7 1 3

2 9 7 7 7

1, 3

Notes

5 4 6

3 4 2

x y

x y

Ex.


2) Make opposites.




2x

2, 1 5) Check your answer.

2 4x 2 2

5 4 6x y 5 4 6y 2

10 10 4 4y 4 4

1y

10 4 6y

Now you try.

Notes

5 4 6

3 4 2

x y

x y

Ex.


2) Make opposites.





5 4 6x y 5 4 6 2 1

10 4 6

Check

6 6

3 4 2x y 3 4 2 2 1

6 4 2 2 2

2, 1

Notes

3 5 2

3 6 6

x y

x y

Ex.


2) Make opposites.




4y

6, 4 5) Check your answer.

1 4y 1 1

3 5 2x y 3 5 2x 4

20 20 3 18x 3 3

6x

3 20 2x

Now you try.

Notes

Ex.


2) Make opposites.





3 5 2x y 3 5 2 6 4

18 20 2

Check

2 2

3 6 6x y 3 6 6 6 4

18 24 6 6 6

3 5 2

3 6 6

x y

x y

6, 4

Notes

6 7 10

6 7 10

x y

x y

Ex.


2) Make opposites.




Infinite Solutions


0 0

Notes

5 8 9

5 8 2

x y

x y

Ex.


2) Make opposites.




No Solution


0 11

Now you try.

Summary

When a linear system already has ________ just add up both equations and solve for one of the variables. Next plug that solution back into any of the original _________ to find the other ________.

opposites

equations variable

Today’s Homework

1. Pencil ONLY.2. Must show all of your work.

• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.

Rules for Homework

Homework 6.3A

2 5 21.

2 3 18

x y

x y


4 12.

2

x y

x y

4 3 73.

4 2 2

x y

x y

2 54.

3 2 11

x y

x y

5 6 45.

2 6 2

x y

x y

3 146.

2 1

x y

x y

6 2 27.

6 2 4

x y

x y

3 138.

4 16

x y

x y

5 4 139.

5 4 13

x y

x y

3 710.

1

x y

x y

2 2 1811.

2 9

x y

x y

5 2 1612.

2 8

x y

x y

Complete the Ticket Out the Door without talking!!!!!

Talking = time after the bell!

Ticket Out the Door

Put your NAME on the paper.

When finished, turn your paper face DOWN.

Solve the system.

2 3 6

2 2 14

x y

x y

bell work 2/11/2015 solve the system by substitution

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