Systems with Elimination

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

To eliminate the x variables

• multiple the top equation by -1

• multiply the bottom equation by 4

• multiply the bottom equation by -4

• multiply the bottom equation by -1

To eliminate the y variable, . . .

• subtract the equations

• add the equations

• multiply the bottom equation by -1 and then add the equations together

Solve this system by elimination

• (0,2)

• no solution

• (2,0)

To solve this by elimination, which of the follow answer choices show an accurate strategy that will eliminate a variable.

• Multiply the top equation by -3 and then add the equations together.

• multiply the top equation by -3 and multiply the bottom equation by +5. Then, add the equations together.

• multiply the top equation by +9 and multiply the bottom equation by -4. Then, add the equations together.

• multiply the top equation by 9 and multiply the bottom equation by 4. Then, add the equations together.

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 
• Infinite number of solutions  
• (−6, 10) 
• (6, 4) 

Solve the system by elimination.  

4x + 12y = −1
−3x − 9y = 0 

• (10, 1) 
• (−10, −1) 
•  (10, −1) 
•  No solution