Elimination Review

Elimination Review

By Reed Carbone

​Goal: To Eliminate one of the variables so we can solve for the other.

​Step 1: Line up your two equations one on top of the other so your "x's" are above your "x's" and your "y's" are above your "y's". Your constants should also be above your constants.

Step 2: Add (or subtract) your like terms to cancel out one of your variables. (Note: if you cannot cancel one of your variables, you will need to multiply one of your equations by a constant so that you can cancel.)

Step 3: Solve the resulting equation for your remaining variable.

Step 4: Plug that solution back into one of your equations to solve for the other variable.​

​Solve the system:

2x - 4y = 3

6 + 8y = 4x​

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

Multiple Choice

y - 13 = 5x

y - 5x = 12

• Infinitely Many Solutions

• No Solution

• (-2,3)

• _3,-2)

Multiple Choice

y = 2x + 10

3y - 6x = 30

• Infinitely Many Solutions

• No Solutions

• (5,5)

• (-5,-5)

Multiple Choice

$$y\ -\ \frac{1}{4}x\ =\ -1$$  

$$y\ -\ 2\ =\ 4x$$  

• Infinitely Many Solutions

• No Solutions

• $$\left(-\frac{6}{5},-\frac{4}{5}\right)$$  

• $$\left(-\frac{4}{5},-\frac{6}{5}\right)$$  

Multiple Choice

A customer bought 2 boxes of popcorn and 3 drinks for $12. Another customer bought 3 boxes of popcorn and 5 drinks for $19. How much does a box of popcorn cost? How much does a drink cost?

• Popcorn: $3

  Drink: $2

• Popcorn: $2

  Drink: $3

• Popcorn: $5

  Drink: $7

• Popcorn: $7

  Drink: $5

Multiple Choice

Taxi A charges a fee of $3.50, plus $1.75 per mile. Taxi B charges a fee of $1.25, plus $2.00 per mile. At what distance would the taxis cost the same?

• 2 miles

• 5 miles

• 9 miles

• 15 miles

Multiple Choice

6x + 3y = 24

y = -2x + 8

• Infinitely Many Solutions

• No Solutions

• (2,4)

• (3,2)