Unit Test

Which is the approximate solution to the system y = 0.5x + 3.5 and y = −x + shown on the graph?

(-2.7, 2.1)

What is the solution to the system of equations?

(0, -5) (where the lines intersect)

What is the solution to this system of linear equations? 7x - 2y = -6 8x + y = 3

(0, 3)

What is the solution to the system of equations? y = -5x + 3 y = 1

(0.4, 1)

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian spent a total of $26.50. The book costs can be represented by the system of equations below. h+p=251.50h+0.50p=26.50

11

What is the value of y in the solution to the system of equations? x + y = 1 2x - 3y = -30

8

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?

a + b ≥ 30 b ≥ a + 10

At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

x + y > 12

Which linear inequality is represented by the graph?

y > x + 3

Which system of linear inequalities is represented by the graph?

y > x - 2 and x + 2y < 4

Which linear inequality is represented by the graph?

y ≤ 1/3x - 1.3

Which inequality pairs with y≤−2x−1 to complete the system of linear inequalities represented by the graph?

y>−2x+2

The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −203x + 5y = 59→3x + 5y = 59 13x = 39 Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

13x = 39

A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?

12 ≤ 2x + 3y

Which description of the graph of the linear inequality y ≥ 7x - 4 is correct?

The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

Which ordered pair makes both inequalities true? y < 3x - 1 y > -x + 4

(4,0)

What is the solution to this system of linear equations? x + y = 4 x − y = 6

(5, −1)

What is the solution to this system of linear equations? 3x - 2y = 14 5x + y = 32

(6, 2)

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

60 inches

y=5x - 1-15x - 3y=3 How many solutions does this linear system have?

one solution: (0, -1)

A system of inequalities, where x is the rate of a spaceship in a video game and y is where the ship travels on the screen in 3.5 seconds, is represented by the graph. Which symbol could be written in both circles in order to represent this system algebraically? y 3x x -2

≥