Solving Systems by Elimination

Solving Systems by Elimination

By Zanier Fuller

• Linear Combination

• Graphing​

Methods to Explore

• Using Tables

• ​Using Substitution

Methods We've Done

Solving Systems

Quiz will be Friday, Feb 18th. Tomorrow we have stations to practice each skill.

1. line up the x & y & the equal sign.

2. look to see if the variables are the same/opposite.

   1. if YES - Move to Step 3

   2. If NO. - multiply one or both equation by a constant (LCM) to make the coefficients the same or opposite.

3. Add or Subtract the TWO equations to eliminate one of the variables.

4. Solve for the remaining variable

5. Sybstitute your answer in one of the original equations

6. Check your answer.

7. Write final answer as an ordered pair.

STEPS TO SOLVE

Let's Explore Each Step

line up the x & y & the equal sign.​

Multiple Choice

Look at the system below. Is the x & y lined up?

$$3x=4y-7\$$  

$$3x+7y=11$$  

• YES

• NO

Multiple Choice

Is the System Lined up?

$$4y\ -\ 3x=12$$  

$$y+3x=0$$  

• No

• YES

Let's Explore Each Step

look to see if any of the coefficients are the same/opposite.

Multiple Choice

Are any of the coefficients same or opposite?

2x - 6y = 20

2x + 5y = -11

• Same

• Opposite

• Neither

Multiple Choice

Are any of the coefficients same or opposite?

5x - 2y = 11

-10x + 3y = -4

• Same

• Opposte

• Neither

Multiple Choice

Are any of the coefficients same or opposite?

x - y = 11

2x + y = 19

• Same

• Opposite

• Neither

Multiple Choice

Are any of the coefficients same or opposite?

4x+ 9y = 28

-4x -y = -28

• Same

• Opposite

• Neither

Multiple Choice

Solve the system:

x + 6y = 17

x + 3y = -8

• Same

• Opposite

• Neither

Let's Explore Each Step

If NO. - multiply one or both equation by a constant (LCM) to make the coefficients the same or opposite.

Let's Explore Each Step

Add or Subtract the TWO equations to eliminate one of the variables.

Multiple Choice

9x-3y=-3

-5x+3y=-1

Would you add or subtract to eliminate the variable (Get ZERO)

• ADD

• SUBTRACT

Multiple Choice

10x-8y=-30

-10x+9y=25

Would you add or subtract to eliminate the variable (Get ZERO)

• ADD

• SUBTRACT

Multiple Choice

Would you add or subtract to eliminate the variable (Get ZERO)

x + y = 3

x - 10y = -30

• ADD

• SUBTRACT

Multiple Choice

Would you add or subtract to eliminate the variable (Get ZERO)

-10x-9y=9

10x+7y=-7

• ADD

• SUBTRACT

Multiple Choice

Would you add or subtract to eliminate the variable (Get ZERO)

-2x+7y=0

2x+7y=-16

• ADD

• SUBTRACT

• EITHER

Let's Explore Each Step

​

ONE VARIABLE MUST BE ELIMINATED!!!!!!!!!

​

Multiple Choice

4x +  8y = 20
-4x + 2y = -30
Which variable will be eliminated?

• The  x
• The  y
• The  z
• The unknown

Multiple Choice

What is the first step in solving a system of equations by elimination?

• line up the like terms.

• Get both equations in slope-intercept form.
• Get both equations equal to zero.
• Put the x terms first.

Multiple Choice

Which variable will be eliminated?

4x+9y=28

4x-y=-28

• all of the variables

• none of the variables

• y

• x

Multiple Choice

Which variable will be eliminated

3x+7y=23

-3x-7y=-17

• all of them

• none of them

• x

• y

Multiple Choice

Which variable will be eliminated?

-9x+4y=-20

5x+4y=4

• all of the variables

• none of the variables

• y

• x

Multiple Choice

Which variable will be eliminated

7x+y=-9

-3x-y=5

• all of the variables

• none of the variables

• x

• y

Multiple Choice

Which variable will be eliminated?

4x+4y=4

3x+4y=10

• x

• y

• both

• im lost

Multiple Choice

Which will be eliminated?

-x+2y=17

2x+2y=-10

• y

• x

• both

• still lost

Let's Get Ready to Try on Paper