556 Final Exam
and− 4 x+y=− 2How can we add multiples of these two equations to make x vanish, leaving us with a
solvable first-degree equation in y alone, with coefficients that are all integers?
(a) We can’t.
(b) We can multiply the top equation through by 2, and then add it to the bottom equation.
(c) We can multiply the bottom equation through by −1/2, and then add it to the top
equation.
(d) We can multiply both equations through by 2, and then add them.
(e) We can multiply both equations through by 0, and then add them.- All of the following equations except one are generally true for any two integers p and
q. Which one is the exception?
(a)p+q=q+p
(b)p+ (−q)= (−q)+p
(c) (−p)+q=q+ (−p)
(d)p−q=q−p
(e) (−p)+ (−q)= (−q)+(−p) - Suppose that m and n are integers, and p and q are nonzero integers. Which of the
following statements is always true?
(a) If m/p=n/q, then mq=np.
(b) If m/p=n/q, then mn=pq.
(c) If m/p=n/q, then mp=nq.
(d) If m/p=n/q, then m/q=n/p.
(e) None of the above. - Suppose a,b, and c are single digits, all different. What is the fractional equivalent of
the endless repeating decimal 0.abcaabcaabcaabca ...?
(a)a,bca / 9,999
(b)c,aab / 9,999
(c)a,abc / 9,999
(d)b,caa / 9,999
(e) None of the above - Fill in the blank to make the following statement true. “Suppose that a is a nonzero
number. Consider am and an, where m and n are integers. If we multiply these two
quantities, we get the same result as if we ____.”
(a) divide a by (m+n)
(b) multiply a by (m+n)
(c) raise a to the power of (m+n)