Systems of Equations and Inequalities Review

The sum of two positive integers, a and b, is at least 30.

The difference of the two integers is at least 10.

• a + b ≥ 30 b ≥ a + 10

• a + b ≥ 30 b ≤ a – 10

• a + b ≤ 30 b ≥ a + 10

• a + b ≤ 30 b ≤ a – 10

The solutions to the inequality y > −3x + 2 are shaded on the graph. Which point is a solution?

• (0, 2)

• (2, 0)

• (1, −2)

• (−2, 1)

How many solutions does this linear system have?

y = x + 2

6x – 4y = –10

• one solution: (–0.6, –1.6)

• one solution: (–0.6, 1.6)

• no solution

• infinite number of solutions

Which system is represented by the graph?

• y ≥ 2x

  x + 2y < –8

• y > 2x

  x + 2y ≤ –8

• y < 2x

  x + 2y ≥ –8

• y ≤ 2x

  x + 2y > –8

A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. A private contractor charges $75 per hour to develop a logo plus a $100 supply fee.

Which equation can be solved to determine x, the number of hours after which the costs would be the same?

• 50x + 250 = 75x + 100

• 50 + 250x = 75 + 100x

• 50x + 100 = 75x + 250

• 50 + 100x = 75 + 250x

Dance World: y = 15x

Toe Tappers: y = 25 + 12.5x

How many classes would Gina need to take for the total cost to be the same at both dance studios?

• 10

• 15

• 100

• 150

Which symbol could be written in both blanks in order to represent this system algebraically?

y  ____ 3x
 x  _____ –2

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

• t ≤ 40

  p ≤ 184

• t ≤ 40

  8p ≤ 184

• t ≤ 40

  p + 8t ≤ 184

• t ≤ 40

  8p + t ≤ 184

Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l.

w ≥ 0.5l

2l + 2w ≤ 180

What is the maximum length possible for her blanket?

Which ordered pairs make both inequalities true? Select two options.

y < 5x + 2

y > 1/2x + 1

• (–1, 3)

• (0, 2)

• (1, 2)

• (2, –1)

• (2, 2)