Systems - Elimination

In the elimination method you either add or subtract the equations to get an equation in one variable.

• True

• False

Answer explanation

This is true! Subtracting the equations is the same as when we multiply by a -1 first to get opposite coefficients.

Identify the property 
a + (-a) = 0

• Inverse of addition 
• Identity of addtion
• associative of addition 
• symmetric

Tags

CCSS.7.EE.A.1

What is the additive inverse of 2/3?

• -2/3

• 3/2

• 2/3

• -3/2

Tags

CCSS.7.NS.A.1B

What is the additive inverse of -5

Answer explanation

Adding these two numbers together would give us 0!

Any number you multiply by zero is equal to zero.

• True

• False

Answer explanation

This why when you have additive inverses

-3x + 3x = 0x

and if 0 * anything is 0

then 0x = 0

This is why you never see 0x

The elimination method works best when

• the equations are funny looking

• the equations are written in standard form

• the equations have isolated variables

• The equations make math

If you add these equations together which variable is going to eliminate?

• x

• y

• 4

Answer explanation

-4x + 4x = 0x = 0

After you eliminate the x variables, you can solve for y. 

Do it! What do you get?

•  $y=6$  

•  $y\ =\ 1.2$  

•  $y=-4$  

•  $y=-6$  

Once you find that y = -6, you can plug -6 in for y into either equation. Once you do this, simplify and solve for x. What do you get?

• $x=6$

• $x=-6$

• x = 0

To eliminate the y variable, . . .

• multiply the top equation by 1

• multiply the bottom equation by 3

• multiply the bottom equation by -3

• multiply the top equation by 4