5.2 Systems Elimination and Word Problems

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

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740
• S + A = 530
  4S + 3A = 1740
• S + A = 1740
  3S + 4A = 530
• S + A = 1740
  4S + 3A = 530

What do you get for y when you start solving

• 2

• -1

• 1

• -2

Solve for x

• 1

• -2

• -1

• -6

Which variable would be the BEST choice to try and eliminate?

• x

• y

What does the new equation become after multiplying?

• -12x + 6y = 26

• -12x + 18y = 26

• -12x + 18y = 78

What should we try and get the coefficients of y to be?

• 15 & -15

• 10 & -10

• 8 & -8

When using the elimination method to solve the system of equations 2x + 5y = 10 and 3x - 5y = 15, what is the resulting equation after the first step?

• 5x = 25

• 5x + 10y = 20

• 5x = 20

• 6x = 30

When using the elimination method to solve the system of equations 4x + 3y = 20 and 2x - 3y = 10, what is the resulting equation after the first step?

• 3x + 3y = 30

• 2x = 20

• 6x = 30

• 5x = 25

When applying the elimination method to the system of equations 5x - 2y = 10 and 10x + 2y = 40, what is the resulting equation after the first step?

• 15x = 50

• 5x = 15

• 15x + 4y = 50

• 10x = 30