Systems of Linear Equations Review

What is the solution to this system of equations?

• (1,0)

• (-3, -1)

• (-1,-3)

• (1,3)

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

Homer sells tickets for admission to the school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Write a system to represent this situation assuming "a" represents # of adult tickets and "c" represents # of children's tickets.

• a + c = 21

  6a + 4c = 104

• a + c = 104

  6a + 4c = 21

• a + c = 21

  6c + 4a = 104

• a + c = 104

  6c + 4a = 21

Enterprise charges to rent compact cars for a fixed amount per day plus a fixed amount for each mile driven. Batman rented a car for 6 days, drove it 550 miles and spent $337. Superman rented the same car for 3 days, drove for 350 miles and spent $185. Set up the system. Let "d" represent the fixed charge per day and "m" represent the cost per mile.

• 6d + 550m = 337

  3d + 350m = 185

• 6d + 550m = 185

  3d + 350m = 337

• 6m + 550d = 337

  3m + 350d = 185

• 6m + 550d = 185

  3m + 350d = 337

The sum of twice a number x and three times a number y is 69. The different between four times number x and twice number y is 18. What are the numbers x and y?

• 2x + 3y = 69 and 4x - 2y = 18

  x = 15 and y = 12

• 3x + 2y = 69 and 4x - 2y = 18

  x = 16 and y = 12

• 2x + 3y = 69 and 4x - 2y = 18

  x = 12 and y = 15

• 3x - 2y = 69 and 4x + 2y = 18

  x = -16 and y = 12

Write the system of equations from the tables.

Hint: find the slope and y-intercept for each table.

What is the solution?

• (5, 11)

• (2, 5)

• (-1, 1)

• (11, 5)

Identify the two equations for the system given in the tables.  Select 2 equations. 

What is the solution to this system of equations?

• (3,-3)

• (-3,3)

• (0,1)

• (1,0)

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines

• Same line

• Parallel lines

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution 

• (6, -2)