Solving Systems and Applications

On Monday, Finley bought 10 cups of coffee and 5 donuts for $16.50. On Tuesday, she bought 5 cups of coffee and 10 donuts for a total of $14.25. Which system could be used to determine the cost of the coffee?

• 10x + 5y = 14.25

  5x + 10y = 16.50

• 10x + 5y = 16.50

  5x + 10y = 14.25

• x + y = 16.50

  x + y = 14.25

• x + y = 30

  15x + 15y = 30.75

Kiley went to the grocery story and bought 4 apples and 6 bananas for $13. Later that week, she purchased 3 apples and 7 bananas for $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

How would you solve the system? Choose all that apply.

• Substitution

  (Rewrite the 1st equation to solve for y)

• Substitution

  (Rewrite the 2nd equation to solve for y)

• Elimination

  (Multiply the second equation by -2)

• Elimination

  (Multiply the second equation by 2)

What could be the first step in solving the system? CHOOSE TWO!

-10x + 3y = 5

x = y - 4

• Substitute y - 4 into the first equation for y

• Substitute y - 4 into the first equation for x

• Rewrite the second equation in standard form then multiply it by -3 to eliminate y

• Rewrite the second equation in standard form then multiply it by 3 to eliminate y

Which of these strategies would eliminate a variable in the system? Choose all that apply.

• Multiply the first equation by 7 then add the equations to eliminate x

• Multiply the first equation by 7 then add the equations to eliminate y

• Multiply the second equation by 6, then add the equations to eliminate x

• Multiply the second equation by 6, then add the equations to eliminate y

Which system of inequalities matches the graph?

• y > 2x - 4

  y < 2

• y < 2x - 4

  y < 2

• y > 2x - 4

  y < 2

• y < 2x - 4

  y < -2

Movie tickets are $4 for the early show (x) and $7 the rest of the day(y). One day, the theater sold 578 tickets and collected $3365 in total ticket sales. Which system represents the situation?

• 4x + 7y = 578

  x + y = 3365

• 4x + 7y = 3365

  x + y = 578

• 4y + 7x = 578

  x + y = 3365

• 7x + 4y = 3365

  x + y = 578

What is the solution to this system?

y = -2x - 6

-2x + y = 6

• (0, -3)

• (-3, -12)

• (-3, 0)

• (3, -12)

There are 41 horses and chickens on a farm. Between them, there are 132 legs. Which system could you use to find out how many of each animal there is on the farm?

• x = 2y + 132

  4x = y + 41

• 4x + 2y = 41

  x + y = 132

• x + y = 41

  4x + 2y = 132

• 2x - 4y = 132

  x - y = 41

Val is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents this situation?

• x - y = -10

  x + y = -2

• x = -2

  y = 5

• x + y = -2

  x - y = -10

• x + y = -10

  x - y = -2