Mathematics 6

MTH 125 Homework Ex for Week 6

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Decide whether the ordered pair is a solution of the given system.

1) x + y = 7

x - y = 3 ; ( -5, 2) 1) _______

A) Yes B) No

Solve the system by graphing.

2) -2x + 3y = -1

3x + 2y = 21

2) _______

A) {( 3, 5)} B) {( -2, 27)}

C) {( 5, 3)} D) ∅; inconsistent system

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.

3) x = 22 - 4y

5x + 3y = 8 3) _______

A) {( 2, 7)} B) ∅; inconsistent system

C) {( -2, 6)} D) {( -3, 7)}

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so.

4) x + 4y = 13

2x + 3y = 6 4) _______

A) {(3, 5)} B) {(-3, 4)}

C) {(-4, 5)} D) ∅; inconsistent system

Tell how many solutions the system has. Do not actually solve.

5) 4x - 16y = 12

y = x - 5) _______

A) Infinitely many B) No solution C) One solution

Solve the problem.

6) Emilia doesn't trust banks, so her savings are hidden under her mattress. Deepak has his savings in an investment

at simple interest. During which year did they have the same amount?

6) _______

A) 1996 B) 1988 C) 1989 D) 1986

Solve the system of equations.

7)

- = 7) _______

A) B) {( -5, 8}) C) {( 5, 8}) D) ∅

Solve by any method. Assume a and b represent nonzero constants.

8) 7ax - 2y = 2

y = 5ax 8) _______

A) B) C) D)

Solve the system of equations.

9) x - y + z = 8

x + y + z = 6

x + y - z = -12 9) _______

A) {(-2, -1, -9)} B) {(2, -1, 9)} C) {(2, -1, -9)} D) {(-2, -1, 9)}

Solve the problem.

10) The perimeter of a rectangle is 60 m. If the width were doubled and the length were increased by 15 m, the

perimeter would be 108 m. What are the length and width of the rectangle? 10) ______

A) Length: 15 m; width: 15 m B) Length: 21 m; width: 9 m

C) Length: 9 m; width: 21 m D) Length: 15 m; width: 10 m

11) Andy has 27 coins made up of quarters and half dollars, and their total value is $ 9.25. How many quarters does he

have? 11) ______

A) 12 quarters B) 17 quarters C) 10 quarters D) 22 quarters

12) The speed of a stream is 6 mph. If a boat travels downstream in the same time that it takes to travel

upstream, what is the speed of the boat in still water? 12) ______

A) 18 mph B) 20 mph C) 12 mph D) 21 mph

13) A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower

than the power boat. Find the speed of each boat. 13) ______

A) Power boat: 15 mph; cabin cruiser: 10 mph

B) Power boat: 10 mph; cabin cruiser: 5 mph

C) Power boat: 20 mph; cabin cruiser: 15 mph

D) Cannot be determined without more information

14) A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies

experience production decline over the period shown in the graph?

14) ______

A) Company A B) Company A and Company C

C) Company C D) Company B and Company C

Solve the system by substitution or elimination. If a system is inconsistent or has dependent equations, say so.

15) y = - x

-5x + 4y = 7 15) ______

A) B)

C) D) ∅; inconsistent system