Algebra Know-It-ALL

552 Final Exam

(d) Three.

(e) Infinitely many.

27. Which of these integers is the smallest?
    (a)− 8
    (b)− 2
    (c) 0
    (d) 3
    (e) 7


28. Which of these integers has the largest absolute value?
    (a)− 8
    (b)− 2
    (c) 0
    (d) 3
    (e) 7


29. Imagine a two-by-two linear system in variables x and y. Suppose the graphs of the
    equations are parallel, but not coincident, lines in Cartesian coordinates, where y is the
    dependent variable. Such a system has
    (a) solutions corresponding to the y-intercepts of the lines.
    (b) solutions corresponding to the x-intercepts of the lines.
    (c) solutions corresponding to the x-intercept of one line and the y-intercept of the
    other line.
    (d) no solutions.
    (e) infinitely many solutions.


30. Consider the following pair of equations as a two-by-two system:

y=a 1 x+b 1

and

y=a 2 x^2 +b 2 x+c

where a 1 ,a 2 ,b 1 ,b 2 , and c are real numbers, and neither a 1 nor a 2 are equal to 0. What

are the smallest and largest numbers of elements that the solution set of such a system

can have?

(a) None, and one.

(b) None, and two.

(c) None, and three.

(d) One, and three.

(e) None, and infinitely many.