7. Systems of Equations &amp; Matrices

Multiple Choice

Graph the system of inequalities and indicate the region (if any) of solutions satisfying all equations.

$x+y\le4$

$y\ge1$

$x>0$

203

Graph the solution set of each system of inequalities.

$x\le4$

$x\ge0$

$y\ge0$

$x+2y\ge2$

Graph the solution set of each system of inequalities.

$2y+x\ge-5$

$y\le3+x$

$x\le0$

$y\le0$

4

Graph the solution set of each system of inequalities.

$2x+3y\le12$

$2x+3y>-6$

$3x+y\lt{4}$

$x\ge0$

$y\ge0$

Graph the solution set of each system of inequalities.

$y>x^2+2$

$y\le x-2$

Graph the solution set of each system of inequalities.

$3x-2y\ge6$

$x+y\le-5$

$y\le4$

Graph the solution set of each system of inequalities.

$y\le x^3-x$

$y>-3$

5

Graph the solution set of each system of inequalities.

$y\ge3^{x}$

$y\ge2$

Graph the solution set of each system of inequalities.

$y\le\log x$

$y\ge\left|x-2\right|$

7

Graph the solution set of each system of inequalities.

$e^{x}-y\le1$

$x-2y\ge4$

6

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

85

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

This

is a piecewise function. Refer to the textbook.

52

In Exercises 39–45, graph each inequality. y ≤ 2^x

73

In Exercises 39–45, graph each inequality. y ≤ x^2 - 1

46

In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

92

In Exercises 39–45, graph each inequality. 3x - 4y > 12

60

Graph each inequality. x + 2y ≤ 6

9

Graph each inequality. 4y - 3x ≤ 5

7

Graph each inequality. x < 3 + 2y

35

Graph each inequality. 2x > 3 - 4y

38

Graph each inequality. x ≤ 3

36

Graph each inequality. y < 3x^2 + 2

21

Graph each inequality. y > (x - 1)^2 + 2

Graph each inequality. x^2 + (y + 3)^2 ≤ 16

24

Graph each inequality. y > 2^x + 1

19

Graph each inequality. y ≤ log(x - 1) - 2

Work each problem. Write the inequality that represents the region inside a circle with center (-5, -2) and radius 4.

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

105

Graph the solution set of each system of inequalities. x + y ≥ 0 2x - y ≥ 3

63

Graph the solution set of each system of inequalities. 2x + y > 2 x - 3y < 6

21

Graph the solution set of each system of inequalities. 3x + 5y ≤ 15 x^2 + y^2 < 9

25

Graph the solution set of each system of inequalities. 4x - 3y ≤ 12 y ≤ x^2

34

Graph the solution set of each system of inequalities. x + 2y ≤ 4 y ≥ x^2 - 1

45

Graph the solution set of each system of inequalities. y ≥ (x - 2)^2 + 3 y ≤ -(x - 1)^2 + 6

42

Graph the solution set of each system of inequalities. y ≥ x^2 + 4x + 4 y < -x^2

97

In Exercises 1–26, graph each inequality. x+2y≤8

36

In Exercises 1–26, graph each inequality. x−2y>10

65

In Exercises 1–26, graph each inequality. y≤(1/3)x

45

In Exercises 1–26, graph each inequality. y>2x−1

48

In Exercises 1–26, graph each inequality. x≤−3

43

In Exercises 1–26, graph each inequality. y>−3

45

In Exercises 1–26, graph each inequality. x^2+y^2≤1

48

In Exercises 1–26, graph each inequality. x^2+y^2>25

43

In Exercises 1–26, graph each inequality. (x−2)^2+(y+1)^2<9

85

In Exercises 1–26, graph each inequality. y

39

In Exercises 1–26, graph each inequality. y≥x^2−9

78

In Exercises 1–26, graph each inequality. y≥log_2(x+1)

41

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+6y≤6, 2x+y≤8

36

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 2x−5y≤10, 3x−2y>6

60

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. y>2x−3, y<−x+6

43

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x+2y≤4, y≥x−3

98

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x≤2, y≥−1

95

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. −2≤x<5

88

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x−y≤1, x≥2

54

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x+y>4, x+y<−1

74

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x+y>4, x+y>−1

125

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. y≥x^2−1, x−y≥−1

78

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x^2+y^2≤16, x+y>2

22

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x^2+y^2>1, x^2+y^2<16

23

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. (x−1)^2+(y+1)^2<25, (x−1)^2+(y+1)^2≥16

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x^2+y^2≤1, y−x^2>0

21

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x^2+y^2<16, y≥2^x

39

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x−y≤2, x>−2, y≤3

24

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+y≤6, 2x−y≤−1, x>−2, y<4

28

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x≥0, y≥0, 2x+ 5y< 10, 3x + 4y ≤ 12

25

In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.

20

In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.

46

In Exercises 65–68, write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is no more than 2. The y-variabe is no less than the difference between the square of the x-variable and 4.

27

In Exercises 69–70, rewrite each inequality in the system without absolute value bars. Then graph the rewritten system in rectangular coordinates. |x|≤2, |y|≤3

23

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

40

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

70

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?

32

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 3x + 5y

8

The graphs show regions of feasible solutions. Find the maximum and minimum values of each objective function. objective function = 3x + 5y

8

Find the maximum and minimum values of each objective function over the region of feasible solutions shown at the right. objective function = 10y

10

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=5x+6y

253

In Exercises 1–4, find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=40x+50y

71

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

73

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

61

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

52

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

118

In Exercises 5–14, an objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

179