9. Solve the system by the substitution method. If a unique solution does not exist, state whether the system is inconsistent or dependent.
5x – 15y = 10
x = 3y + 4
A) {(2, 0)}
B) {(–1, 1)}
C) Infinite solutions, dependent system
D) No solution, inconsistent system
10. Ann has a total of 100 coins in her jar. The coins inside the jar are either quarters or dimes. The total amount in the jar is $14.50, how many of each type of coin is in the jar?
A) 30 dimes and 70 quarters
B) 80 dimes and 20 quarters
C) 70 dimes and 30 quarters
D) 75 dimes and 25 quarters
11. True or False: (1, –2, 3) is a solution to the equation 3x + y – 3z = –7.
12. Which of the following is a solution to the equation –4x + 3y – z = 29?
A) (–2, 2, 4)
B) (–4, 3, –4)
C) (0, 0, 29)
D) (4, –4, 3)
15. Geometrically, a dependent solution to a linear system of three equations in three variables can be seen as:
A) Three planes intersecting at a point
B) Three planes intersecting in a line
C) Three parallel planes
D) Three planes that don't intersect
16. True or False: Geometrically, an inconsistent linear system of three equations in three variables can be seen as three planes intersecting at a point.
17. The perimeter of a triangle is 72 inches. If side a is twice the length of side b and and the longest side, c, is equal to the sum of lengths of sides a and b, find the measure of each side.
A) a = 16 in., b = 8 in., c = 32 in.
B) a = 10 in., b = 5 in., c = 30 in.
C) a = 24 in., b = 12 in., c = 36 in.
D) a = 36 in., b = 18 in., c = 42 in.
18. Adult tickets for a play cost $9 and child tickets cost $8. If there were 23 people at a performance and the theater collected $193 from ticket sales, how many children attended the play?
A) 15 children B) 13 children C) 9 children D) 14 children
19. The length of a rectangle is 3 in. more than twice its width. If the perimeter of the rectangle is 36 in., find the width of the rectangle.
A) 7 in. B) 6 in. C) 4 in. D) 5 in.
20. Lane invested $22,000, part at 8% and part at 7%. If the total interest at the end of the year is $1,710, how much did she invest at 8%?
A) $18,000 B) $16,000 C) $5,000 D) $17,000