Algebra Unit 6 Systems of Equations and Inequalities

Which of the following is not a solution to this system of inequalities?

• (0,-1)

• (0,3)

• (4,0)

• (6,-2)

What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 

• 1

• -1

• 3

• 4

The graph shows the distance that Car A and Car B are from Dallas over a five-hour period. Car A is driving toward Dallas. Car B is driving away from Dallas. Based on the graph, how far from Dallas will the two cars be when they are the same distance from Dallas?

• It will take 3 hours for

  them to be the same distance from Dallas.

• They will be 275 miles

  from Dallas when they are

  the same distance away.

• They will be 225 miles from Dallas when they are the same distance away

• It will take 5 hours for

  them to be the same distance from Dallas.

The sum of two numbers is 90. The difference of these two numbers is 22. What are the two numbers?

• The smaller number is 34 and the larger number is 56.

• The smaller number is 42 and the larger number is 48.

• The smaller number is 30 and the larger number is 60.

• The smaller number is 40 and the larger number is 50.

Rosie, Steph, and Terri are sisters. Rosie is the oldest and Terri is the youngest. The sum of the three girls' ages is 25. Rosie's age is 5 less than the sum of Steph's and Terri's ages combined. Terri is only 3 years younger than Rosie. What system of equations could be used to determine the three sisters' ages?

• r + s + t = 30

  ( s + t ) - 5 = r

  r + 3 = t

• r + s + t = 25

  ( s + t ) - 5 = r

  r - 3 = t

• r + s + t = 25

  s + t + 5 = r

  r - 3 = t

• r + s + t = 20

  r - 5 = s + t

  r + 3 = t

In a recent academics meet, 10 students from our school placed in their events, earning a total of 21 points. Each first place earned 3 points, each second place earned 2 points, and each third place earned 1 point. The number of second place finishers was the same as the number of first place finishers and third place finishers combined. Which of the following equations would be incorrect when writing a system of equations to determine the number of competitors that placed first (f), second (s), and third (t) ?

• 3f + 2s + 1t = 21

• s = f + t

• f + s + t = 10

• f = s + t

Which of the graphs of a system of linear inequalities below shows that the point (-3, 4) belongs in the solution set?

• 
• 
• 
• 

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)

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

• x+y≤300
  7.5x+5.5y≥2000

• x+y<300
  7.5x+5.5y≥2000

• x+y≤300
  7.5x+5.5y≤2000

• x+y>2000
  7.5x+5.5y≤300