Name:    Linear Systems and Equations

Multiple Choice
Identify the choice that best completes the statement or answers the question.
The following questions are from past SAT exams and different math contests.  Do your best to answer each one.

1.

If   and what is the value of
 a. 0 c. 7 b. 3 d. 9

2.

Chris is purchasing different types of yarn.  He purchases “x” yellow yarn for \$3.49 each, and “y” blue yarns for \$5.52 each, after taxes.  If Chris purchased a total of 14 yarns and spent a total of \$73.22, which of the following sets of equations is true?
 a. c. b. d.

3.

The first number is twice the second.  The sum of five times the first and 1.5 times the second is equal to 17.25.  Which of the following equations represents this system?
 a. c. b. d.

4.

If    and , what is the value of “e”?
 a. 7 c. 11 b. 8 d. 14

5.

If    and , what is the value of
 a. 5 c. 10.5 b. 7.5 d. 15

6.

At a fund raiser, a cake is sold for \$4 and a pie is sold for \$5.  A total of 75 pies and cakes were sold and \$340 was raised.  How many cakes and pies were sold?
 a. c. b. d.

7.

What is the value of     if       ?
 a. c. b. d.

8.

What is the solution to this set?
 a. c. b. No Solutions d. Infinitely Many Solutions

9.

What best describes this set of equations?
 a. Lines are parallel c. Lines intersect at one point b. Lines are perpendicular d. Lines intersect at infinite points

10.

What best describes this set of equations?
 a. Lines are parallel c. Lines intersect at one point b. Lines are perpendicular d. Lines intersect at infinite points

11.

Line “L” contains points   and .  At what point will line “L” intersection with another line “Q” with equation
 a. c. b. These lines do not intersect d. These lines intersect at infinitely many points

12.

A dance studio charges \$8 per student for its morning class and \$16 per student for its evening class. Three times as many students attended the evening class as attended the morning class.  If the dance studio earned \$2,520 on Friday, how many people attended the morning class?
 a. 15 c. 56 b. 45 d. 135

13.

If     and , what is the value of
 a. 4 c. 10 b. 6 d. 14

14.

Line “L” has a slope of zero and a y-intercept of 4.  Line “Q” has a slope that is undefined and an x-intercept of 3.  What is the distance between the origin and the point of intersection between these two lines?
 a. c. b. 4 d. 5

15.

Line “L” passes through points   and .  Line “Q” is given by the equation .  What is the point of intersection of line “L” and “Q”?
 a. c. b. d.

16.

Given the coordinates A , , what is the average of the slopes of ?
 a. c. b. d.