Guided Notes

1

All I Do Is Solve

Verse 1 (0:32) Graphing Method

Warmup Skill: Graph each line.

1) y =12x − 3 2) 8x + 4y = 16

Case 1 Case 2 Case 3

So graph your first line, now graph the other one too

The intersection is your answer, that's all you've got to do

y = 2x − 2y = −x + 4

⎧⎨⎩

, ( )

Sometimes lines are the sameThat's infinite solutions

y = x + 2y = x + 2

⎧⎨⎩

___________ solutions

Sometimes they never touch, no common points producing

y = x + 2y = x − 2

⎧⎨⎩

___________ solutions

Name: _______________________________

Self Check: Solve the following systems by graphing(Self Check Answers: #1: (-3,-1) #2: No Solutions)

1) y = 1

3x

y = −2x − 7

⎧⎨⎪

⎩⎪ 2)

y = 2x + 3

y = 63x − 5

⎧⎨⎪

⎩⎪

Understanding: Explain how the intersection of two lines is a solution for each of those lines.

Verse 2 (1:36) Elimination Method

Warmup Skill: Manipulate the following equations so that each equation has 10x as its initial term.

1) 2x + y = 10 2) −5x + 2y = 6 3) 25x + 1

5y = 2

2

Fill In The BlanksLyrics Fill In The Blanks

On the top and bottom row,Make coefficients both the same,

Get one plus, the other minusThose are the rules of this game

Multiply or divide!That's the only way to get your

coefficients right!These additive inverses wipe out x or y!

Whatever's easier is what you have to decide!

(All we do is solve!)

You solve for x (x!)

Now you solve y (y!)Eliminate with me...cause I'm

always solving right

9x + 4y = 123x + 6y = −3

⎧⎨⎩

⎯ →⎯

x + y =

x + y =

⎧⎨⎪

⎩⎪

54x + 24y = 7212x + 24y = −12⎧⎨⎩ ⎯ →⎯

54x + 24y = 72

x W y = ⎧⎨⎪

⎩⎪

Show Method B and circle the coefficients that cancel

9x + 4y = 123x + 6y = −3

⎧⎨⎩

⎯ →⎯⎯

x W y =

x W y =

⎧⎨⎪

⎩⎪

Show Method F and circle the coefficients that cancel

9x + 4y = 123x + 6y = −3

⎧⎨⎩

⎯ →⎯ x W y =

x W y =

⎧⎨⎪

⎩⎪

+54x + 24y = 72-12x - 24y = 12⎧⎨⎩

x =

x =

3x + 6y = −3↓

3 + 6y = −3

+ 6y = −3

6y =

y =

3

Self Check: Solve the following systems of equations by using the elimination method.(Self Check Answers: #1: (3,0) #2: (-2, 1/2))

1) 5x + 2y = 153x + 3y = 9

⎧⎨⎩

2) 4x + 2y = −74x − 6y = −11

⎧⎨⎩

Understanding: Explain why both multiplying and dividing equations is acceptable when trying to match equations with one another.

Verse 3 (2:39) Substitution Method Warmup Skill: Solve for y in the following equations

1) 2x + y = 10 2) −5x + 2y = 6 3) 25x + 1

5y = 2

4

Lyrics Fill In The Blanks

Get x or y alone on em’

An expression is what you get on em’

Lock it up, block it up, that's the way, you chalk it up

Pardon me I'm teaching up, the pressure up, check it bruh

Plug this in with usLike a cord in a socket

One variable now is all you haveSolve it up, do the math

Find its value,

take it back

The other variable is what you have

Time and time again, when I'm solving systems

Dub South says it best, just solve baby solve

6x − 2y = 26 #13x + 2y = 10 #2

⎧⎨⎩

(Solve for y in equation #1)

6x − 2y = 26

=

+

y = x −

y = ⎡⎣⎢

⎤⎦⎥

(Substitute your expression for y into equation #2) 3x + 2y = 10

3x + 2 ( ) = 10

3x + x − = 10

x − = 10

+ +

x =

x =

y = 3x −13( )→ y = 3 −13

y = −13

y =

x, y( )→ , ( )

5

Understanding: The solution to the system y = 2x +1y = −3x +11

⎧⎨⎩

is (2, 5). Show how you can verify that

(2, 5) is indeed the solution to the system.

Self Check: Solve the following systems of equations by using the substitution method. (Self Check Answers: #1: (4,3) #2: (1, -1/3)

1) 2x − y = 5−3x + 7y = 9

⎧⎨⎩

2) 5x + 3y = 4−2x − 9y = 1

⎧⎨⎩

6

Lyrics Name: ______________________________

All I Do Is Solve

(Chorus)All I do is solve solve solve no matter what

Got systems on my mind, I can never get enoughAnd every time I step up in the classroom

All my students' hands go up!And they stay thereAnd they say yeahAnd they stay there

Up down, up down, up downCause all I do is solve solve solve

And if you solving it put your hands in the air make em stay there!

(Verse 1: Mr. Schultz) GRAPHINGIt's Schultz going in on the verse

Cause I'm solving this system and I won't stop now Get your heads up, eyes on the screen cause I got three ways to get the problem locked

downIt never went no where

But they saying math is backSometimes equations are easy

That's when I like to graphAnd I'm on this systems track, so I spit my graphing flow

The lines slant up or down, like lines with slope should goSo graph your first line, now graph the other one too

The intersection is your answer, that's all you've got to doSometimes lines are the same

That's infinite solutionsSometimes they never touch, no common points producing

Been solving all the time, at South we representCause all I do, all I, all I, all I do is...

(Chorus)

(Verse 2: Mr. Murphy) ELIMINATIONIt's time for me to roll roll

elimination's heresometimes graphing is a no no

when the lines don't cross real clear, so I put down my graph papermy students wanna eliminate, they see it, they say oh boy!

Tell Murphy line it up, On the top and bottom row,

Make coefficients both the same,Get one plus, the other minus

Those are the rules of this game Multiply or divide!

That's the only way to get your coefficients right!These additive inverses wipe out x or y!

Whatever's easier is what you have to decide!(All we do is solve!)You solve for x (x!)

Now you solve y (y!)Eliminate with me...cause I'm always solving right

(Chorus)

(Verse 3: Mr. Winner) SUBSTITUTIONMath in the classroom, variables on the stove

Equations getting heated, systems getting solvedWinner is the teacher, math overload

I've been using substitution since I was 13 years oldGet x or y alone on em

An expression is what you get on emLock it up, block it up, that's the way, you chalk it up

Pardon me I'm teaching up, the pressure up, check it bruhPlug this in with us

Like a cord in a socketOne variable now is all you have

Solve it up, do the mathFind its value, take it back

The other variable is what you haveTime and time again, when I'm solving systems

Dub South says it best, just solve baby solve

(Chorus)

All I Do Is Solve

Verse 1 (0:32) Graphing Method

What is a system?

What is slope?

If a line slants up as it moves to the right, what is the sign of its slope?

If a line slants down as it moves to the right, what is the sign of its slope?

Why are there infinite solutions when the lines are the same?

Why are there no solutions when the lines don’t touch?

Verse 2 (1:36) Elimination MethodWhy is the elimination method sometimes more useful than the graphing method?

What are coefficients?

Why are we able to multiply and divide both sides of an equation by whatever number we choose?

What are additive inverses?

Does it matter what term you eliminate first?

Verse 3 (2:39) Substitution MethodWhen you solve for x or y, what is that variable equivalent to?

What do you do with this expression?

What do you do after you plug this expression in to the other equation?

What do you do after your solve for your first variable?

Discussion Questions/ Lyrical Clarification

Name: ______________________________