Solve Systems with Elimination Steps

What are the steps involved in solving a system of equations using the elimination method?

• Identifying the variable to eliminate, multiplying the equations by appropriate constants, and adding or subtracting the equations to eliminate the variable.

• Dividing the equations by random numbers

• Ignoring one of the equations

• Solving for the variable with no elimination

In the elimination method, what operation is used to eliminate one of the variables?

• Multiplication

• Addition or subtraction

• Division

• Exponentiation

Solve by elimination method.
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

A method to solving a system of equations by getting rid of one of the variables first to solve for the other variable. 

• Graphing Method

• Substitution Method

• Elimination Method

• Drawing Method

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both company's pizza cost the same amount?

• y = 6.80 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30

One brand of suntan lotion comes in a small size with x ounces of lotion and a regular size with y ounces of lotion.  Given the system of equations below how can we eliminate the terms with x?
x+2y = 15
2x + y = 19.5

• subtract the two equations from each other

• multiply the second equation by -1 and add the two equations

• multiply first equation by 2, multiply the second equation by 1 then add them

• multiply the first equation by -2 then add the equations together 

When using any of the 3 methods to solve a system of linear equations the resulting solution is the same no matter which method is used.

• True; using any method will result in the correct solution.

• False; the solution varies because the solution depends on which method is used.

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5

Order the steps of the elimination method:

• Solve for variable

• multiply equation(s) to have opposite coefficients, if necessary

• add vertically

• Align like terms vertically

• Determine the variable to eliminate