Review of Systems of Linear Equations

Solve the system of equations

• Infinite solutions

• (2, -2)

• (1, 0)

• (3, -4)

What is the solution to this system of equations?

• (1,0)

• (-3, -1)

• (-1,-3)

• (1,3)

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

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

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

• Intersecting lines

• Same line

• Parallel lines

If a system of linear equations has 1 solution, the solution is the ____________ of intersection

• slope

• opposite

• point

A system of two identical (overlapping) lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

Write a system of equation to solve the following situation.

Two groups of people order food at a restaurant. one group order 4 pizzas and 7 salads for $34.50. The other group orders 8 pizzas and 3 salads for $30.50. Find the cost of each item.

Let p = pizza and s = salad.

• 4p +7s = 30.50 and 8p + 3s = 34.50

  A pizza costs $2. 40 and a salad costs $3.40

• 4p +7s = 34.50 and 8p + 3s = 30.50

  A pizza costs $2. 50 and a salad costs $3.50

• 4p -7s = 34.50 and 8p - 3s = 30.50

  A pizza costs $1.50 and a salad costs $4.50

• 4p +7s = 34.50 and 8p + 3s = 30.50

  A pizza costs $3.50 and a salad costs $2.50