Bell Work 2/5/14

3 2 121.

2 4

x y

x y

Solve the system by graphing.

1

2m

3

2m

2, 3

2b6b

3 2 12x y 3 3x x

2 3 12y x

2 4x y x x

2 4y x 2 2 2

y 63

2x

2 2 2

y 21

2x

2, 3

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 Substitution (isolated)

04/21/23

Heading

TSWBAT: solve a linear system by substitution when a term is already isolated.

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.

6.2A

Notes• Solving a System of Equations by Substitution

1. Solve one of the equations for x or y.

2. Substitute your new expression from Step 1 into the other equation and solve for the variable.

3. Plug that solved variable into the other equation from Step 1 and solve for the other variable.

4. Check your answers by plugging it into the original equations.

- Get x or y by itself.

Notes

2

5

x

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable x is already by itself.

5x y 5y 2

2 2

7y

2, 7 2, 7

Notes

4

2

y

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable y is already by itself.

2x y 2x 4

4 4

6x

6, 4 6, 4

Now you try.

Notes

3

2 5 1

x

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable x is already by itself.

2 5 1x y 2 5 1y 3

6 6 5 5y

3, 1 3, 1

6 5 1y

5 51y

Notes

1

3 2 8

y

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable y is already by itself.

3 2 8x y 3 2 8x 1

2 2 3 6x

2, 1 2, 1

3 2 8x

3 32x

Now you try.

Notes

2

12

y x

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable y is already by itself.

12x y 12x 2x

3 12x 3 3

4x

Step 32y x 2y 4

8y

4, 8 4, 8

Notes

3

2 4 4

x y

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable x is already by itself.

2 4 4x y 2 4 4y 3y

6 4 4y y

2 2 2y

Step 33x y 3x 2

6x 2 4y 6, 2 6, 2

Now you try.

Notes

2 8

2 5 11

x y

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable x is already by itself.

2 5 11x y 2 5 11y 2 8y 4 16 5 11y y

9 93y

Step 32 8x y 2 8x 3

9 27y

9 16 11y 16 16

6 8x 2x

2, 3 2, 3

Notes

3 4

2 2 16

y x

x y

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable y is already by itself.

2 2 16x y

2 2 16x 3 4x 2 6 8 16x x

8 83x

Step 33 4y x 3 4y 3

8 24x

8 8 16x 8 8

9 4y 5y

3, 5 3, 5

Now you try.

Notes

4 6

2 4

y x

y x

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable y is already by itself.

2 4y x

2 4x 4 6x

2 25x

Step 34 6y x 4 6y 5

2 10x

2 6 4x 6 6

20 6y 14y

5, 14 5, 14

2 2x x

Notes

3 5

4 2

y x

y x

Ex.

Solve the system by substitution.

2) Substitute into other equation.

3) Plug in answer into other equation.

4) Check answer!

1) Solve for x or y.

The variable y is already by itself.

4 2y x

4 2x 3 5x

7 71 x

Step 33 5y x 3 5y 1

7 7x

5 7 2x 2 2

3 5y 2y

1, 2 1, 2

3 3x x

Now you try.

Summary

To solve a linear system by ___________ first _______ the isolated variable in one of the equations. Next plug that expression into the other _________ to find the value of one variable. Finally plug that solution into any of the original _________ to find the other variable.

substitutionidentify

equations

equations

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 6.2A

31.

8

x

x y

Solve the system by substitution.

42.

2 3 2

x

x y

33.

4 2 14

y

x y

24.

9

y x

x y

45.

15

x y

x y

36.

2 4 14

y x

x y

2 57.

3 4 5

x y

x y

3 18.

2 4 16

y x

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 by substitution.

3

2 4 10

x

x y