Multivariable Equations

2) Solve the system of linear equations.

• (-1, 1, 2)

• (2, 1, -1)

• no solution

• infinitely many solutions

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50.  It turns out that the doughnuts were more popular than the coffee.  On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25.  Which equations could be used to determine the cost of the coffee? 

• 10c + 5d = 14.25
  5c + 10d = 16.50

• 10c + 5d = 16.50
  5c + 10d = 14.25

• c + d = 10
  5c + 10d = 16.50

• c + d = 5
  5c + 10d = 16.50

x – y + z = 0

3x – 2y + 6z = 9

–x + y – 2z = –2

• (1,2,3)

• (2,1,3)

• (2,3,1)

• (1,3,2)

Solve

5x + 6y = –10

3x – 2y = –6

• (–2,0)

• (–2,–6)

• (2,0)

• (2,–6)

Solve

−6x − 3y = −15

4x + 2y = 10

• (−6, −4)

• {(x,y)|y = −2x + 5}

• (−6, 10)

• (6, 4)

Solve

−2x − 3y = 3

4x + 6y = −4

• no solution

• (2,0)

• (–4,0)

• (0,0)

Caitlin won a bag full of money! There are ten dollar bills, twenty dollar bills and fifty dollar bills. She has 59 bills in all, with four more twenties than three times the tens. She counts $1530. Write a system of equations to find how many of each bill Caitlin has won.

x = number of $10 bills

y = number of $20 bills

z = number of $50 bills

• x + y + z = 1530

  10x + 20y + 50z = 59

  4y = 3x

• x + y + z = 59

  10x + 5y + z = 1530

  y + 4 = x + 3

• x + y + z = 59

  10x + 20y + 50z = 1530

  y + 4 = 3x

• x + y + z = 59

  x + y + z = 1530

  x + 3y = 4

Erin is three years younger than twice Alex's age. Their ages combined are 33 years. Write a system of equations to determine how old Alex and Erin are.

• x + y = 33

  y = 2x – 3

• x + y = 33

  x = 2y – 3

• x + y = 33

  x = 3 – 2y

• x + y = 3

  x = 33 – 2y