Challenge Solving Systems of Equations

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 

• x + y = 1550
  y  = 4x

• x + y = 1550
  y = x + 4

• y - x = 1550
  y = 4x

• y = 1550 + x
  y = x + 4

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

• x - y = -10
  x + y = -2

• x = -2
  y = 5

• x + y = -2
  x - y = -10

• x + y = -10
  x - y = -2

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49

• x + y = 49
  10x + 5y = 1430 

• x + y = 49
  20x + 50y = 1430

• x + y = 49
  x + y = 1430

The sum of Mr. Micklow and Ms. Craft's age is 55.  The difference is 3.  
Solve:
x + y = 55
x - y = 3

• (26, 23)

• (26, 29)

• (29, 26)

• (29, 32)

The difference of a and b is 3. The sum of the variables is 13. Find the numbers.

• a = 7
  b = 10

• a = 8
  b = 5

• a = 10
  b = 13

If a system of linear equations has no solution, which of the following is NOT true?

• The graph forms parallel lines.

• The lines have the same y-intercept.

• The lines have the same slope.

• The lines do not intersect.

If a system of linear equations has infinite solutions, which of the following is NOT true?

• The graph forms the same line.

• The lines do not intersect.

• The lines have the same slope.

• The lines have the same y-intercept.

Solve the system of equations.

-x + y = -13

-8x - 4y = -8

• (5, 8)

• (5, -8)

• (-5, -18)

• (-5, 8)

• (4,-8)

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

• (0,4)