Today:

Make Up Tests? Complete Class Work

Systems of Equations Today:a. Elimination (3)b. Substitution (2)

c. Solving Systems: Word Problems (2)

Question:

Do you have Friggatriskaidekaphobia?

from Greek tris meaning "3", kai meaning "and",

deka meaning "10" phobos meaning "fear" or "morbid fear"

"Frigg" is the Norse goddess whom Friday is named after

An extraordinary fear of Friday the 13th

Answer honestly...

Determine whether the ordered pair is a solution of the given system.

The ordered pair (5, 2) makes both equations true.

(5, 2) is the solution of the system.

Substitute 5 for x and 2 for y in each equation in the system.

2 – 2 0

0 0

03(5) – 2 13

15 – 2 13

13 13

3x – y 13

(5, 2);

3x – y = 13

𝟐

𝟓x – y = 0

𝟐

𝟓x – y = 0

(–2, 2); x + 3y = 4

–x + y = 2

–2 + 3(2) 4

x + 3y = 4

–2 + 6 44 4

–x + y = 2

– (–2) + 2 2

4 2

Substitute –2 for x and 2 for y in each equation in the system.

The ordered pair (–2, 2) makes one equation true but not the other.

(–2, 2) is not a solution of the system.

If an ordered pair does not satisfy the first equation in the

system, there is no reason to check the other equation(s).

Helpful Hint

SOLVING SYSTEMS BY ELIMINATION:

1. Arrange the like variables in columns.

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.

5x - 4y = -21

-2x + 4y = 18

We need to eliminate (get rid of) a variable by cancelling out one of the variables. We then solve for the other variable.

3x + 0 = -3

x = -1

THEN----

Like variables must be lined under each other.

What should we eliminate first?

Solve: By Elimination

Do we add or subtract the two equations?

5x - 4y = -21

(-1, 4)

Substitute your first

solution into either original

equation and solve for the

second variable.

The solution to this system of equations is:

Now check your answers in both equations------

5(-1) – 4y = -21-5 – 4y = -215 5

-4y = -16 y = 4

5x - 4y = -215(-1) – 4(4) = -21

-5 - 16 = -21-21 = -21

-2x + 4y = 18

-2(-1) + 4(4) = 18

2 + 16 = 18

18 = 18

We have two options; what are they?

x + y = 30x + 7y = 6

We need to eliminate (get rid of) a variable. To simply add this time will not eliminate a variable.

a. Subtract

b. Multiply one of the equations by -1, then add

SOLVING SYSTEMS BY ELIMINATION:

x + y = 30

x + 7y = 6( )-1 -x – 7y = - 6

Now add the two equations and solve.

-6y = 24

- 6 - 6y = - 4

THEN----

x + y = 30

x + y = 30

(34, - 4)

Substitute your answer

into either original

equation and solve for

the second variable.

Solution

Now check your answers in both equations------

x + - 4 =30

+4 +4

x = 34

x + y = 3034 + - 4 = 30

30 = 30

x + 7y = 6

34 + 7(- 4) = 6

34 - 28 = 6 6 = 6

2x - 5y = 2

-3x + 2y = -14

SOLVING SYSTEMS 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.

SOLVING SYSTEMS WORD PROBLEMS:

Kelly went back-to-school shopping this weekend. She

spent $160 on jeans and shirts. She bought a total of

12 items, with jeans costing $16 and shirts costing $12.

How many jeans and shirts did she buy?

1. Mark the text.

2. Label

variables.

j = jeans

s = shirts3. Create

equations.

16j + 12s = 160

What’s the 2nd equation?j + s = 12

4. Solve.

5. Check.

Mrs. Smith took her family and friends to

the movies. There were a total of 12 people.

Children tickets cost $5 and adult tickets cost

$10. She spent a total of $95. How many adults

& how many children went to the movies?

1. Mark the text.

2. Label

variables.

3. Create

equations.

4. Solve.

5. Check.