Linear Situations
Systems
Inequalities
2-Variables
100
If 2x + 3 = 9, what is the value of 6x - 1?
17
100
5x=15
-4x+y=-2
The solution to the given system of equations is (x, y). What is the value of x + y?
A) -17
B) -13
C) 13
D) 17
C) 13
100
The point (8, 2) in the xy-plane is a solution to which of the following systems of inequalities?
A) x > 0; y > 0
B) x > 0; y < 0
C) x < 0; y > 0
D) x < 0; y < 0
A) x > 0; y > 0
100
x + y = 75
The equation above relates the number of minutes, x, Maria spends running each day and the number of minutes, y, she spends biking each day. In the equation, what does the number 75 represent?
A) The number of minutes spent running each day
B) The number of minutes spent biking each day
C) The total number of minutes spent running and biking each day
D) The number of minutes spent biking for each minute spent running
C) The total number of minutes spent running and biking each day
200
The total cost f(x), in dollars, to lease a car for 36 months from a particular car dealership is given by f(x) = 36x + 1,000, where x is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $400?
A) $13,400
B) $13,000
C) $15,400
D) $37,400
C) $15,400
200
The graph of a system of linear equations is shown. What is the solution (x, y) to the system? 
A) (2, 3) B) (3, 4)
C) (4, 5) D) (5, 6)
B) (3, 4)
200
During a portion of a flight, a small airplane's cruising speed varied between 150 miles per hour and 170 miles per hour. Which inequality best represents this situation, where s is the cruising speed, in miles per hour, during this portion of the flight?
A) s<=20
B) s<=150
C) s<=170
D) 150<=s<=170
D) 150<=s<=170
200
Line k is defined by y = 3x + 15. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?
A) -1/3 B) -1/12
C) -1/18 D) -1/45
A) -1/3
300
(b-2)x=8
In the given equation, b is a constant. If the equation has no solution, what is the value of b?
A) 2
B) 4
C) 6
D) 10
A) 2
300
Two customers purchased the same kind of bread and eggs at a store. The first customer paid 12.45 dollars for 1 loaf of bread and 2 dozen eggs. The second customer paid 19.42 dollars for 4 loaves of bread and 1 dozen eggs. What is the cost, in dollars, of 1 dozen eggs?
A) $3.77 B) $3.88
C) $4.15 D) $4.34
D) $4.34
300
y<=x
y<=-x
Which of the following ordered pairs (x, y) is a solution to the system of inequalities above?
A) (1, 0)
B) (-1, 0)
C) (0, 1)
D) (0, -1)
D) (0, -1)
300
A certain apprentice has enrolled in 85 hours of training courses. The equation 10x + 15y = 85 represents this situation, where x is the number of on-site training courses and y is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?
5
400
Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?
A) 3 B) 7
C) 8 D) 12
D) 12
400
2(8x)+4(7y)=12
-2(8x)+4(7y)=12
The solution to the given system of equations is (x, y). What is the value of 8x + 7y?
3
400
Adam’s school is a 20-minute walk or a 5-minute bus ride away from his house. The bus runs once every 30 minutes, and the number of minutes, w, that Adam waits for the bus varies between 0 and 30. Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school?
A) w - 5 < 20
B) w - 5 > 20
C) w + 5 < 20
D) w + 5 > 20
D) w + 5 > 20
400
For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k?
A) (-26/3,0) B) (-9/2,0) C) (-11/3, 0) D) (-17/6, 0)
D) (-17/6, 0)
500
The table shows two values of x and their corresponding values of y. The graph of the linear equation representing this relationship passes through the point (1/4, a) . What is the value of a?
16.25, 65/4
500
ax+by=72
6x+2by=56
In the given system of equations, a and b are constants. The graphs of these equations in the xy-plane intersect at the point (4, y). What is the value of a?
A) 3 B) 4
C) 6 D) 14
D) 14
500
A number x is at most 2 less than 3 times the value of y. If the value of y is -4, what is the greatest possible value of x?
-14
500
The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is (k - 5, b), where k and b are constants. What is the value of b?
33