System of Equations and Inequalities

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

How many solutions does this system of equations have?

• One Solution

• No solution

• Infinitely Many Solutions

• Two Solutions

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Lisa gives child(x) and adult(y) haircuts in her salon. She charges $10 for a child and $40 for an adult haircut. Her goal is to make at least $1000 per week and work no more than 40 hours. The shaded region of the graph represents the possible combinations of adult and child haircuts that will allow her to meet her goal. Which combination represents her maximum profit?

• 10 adult haircuts and 60 child haircuts

• 20 adult haircuts and 40 child haircuts

• no adult haircuts and 80 child haircuts

• 40 adult haircuts and no child haircuts

A city bus collected $1,140 in fares on a given day. The regular fare is $1.50, and the reduced fare is $0.75. If 1,042 total fares were paid, which system of linear equations can be used to find x, the number of regular fares paid, and y, the number of reduced fares paid?

• A

• B

• C

• D

• (1,3)

• (2,1)

• (3,4)

• (6,2)

The equation of the line on the graph is

y = -2x + 1

Find the equation of a second line such that the system has infinitely many solutions.

• y = -2x + 1

• y = -2x + 4

• y = -2(x + 1)

• y = 3x + 8

• y = -2x + 9

The two types of tickets sold at a baseball game are standard tickets and discounted tickets. The price of a discounted ticket was 80% of the price of a standard ticket. There were 153 standard tickets sold at the baseball game. There were 47 discounted tickets sold at the baseball game. The total amount of tickets sales from the standard and discounted tickets was $2,649.34. The line graphed on the grid represents the first equation in a system of linear equations for this situation. If the second equation in the system is y = 0.80x, what is the best estimate of the price of a discounted ticket?

• $13.95

• $14.55

• $13.25

• $11.15

The equation of the line on the graph is

y = -2x + 1

Find the equation of a second line such that the system has no solutions.

• y = -2x + 1

• y = -2x + 4

• y = 2x + 1

• y = 3x + 8

• y = -2(x - 0.5)